Published - 1.9781611975994.73.pdf

Submitted - 1909.12497.pdf

", "abstract": "The classic graphical Cheeger inequalities state that if M is an n \u00d7 n symmetric doubly stochastic matrix, then\n1\u2212\u03bb\u2082(M)/2 \u2264 \u03d5(M) \u2264 \u221a2\u22c5(1\u2212\u03bb\u2082(M)) where \u03d5(M) = min_(S\u2286[n],|S|\u2264n/2)(1|S|\u2211_(i\u2208S,j\u2209S)M_(i,j)) is the edge expansion of M, and \u03bb\u2082(M) is the second largest eigenvalue of M. We study the relationship between \u03c6(A) and the spectral gap 1 \u2013 Re \u03bb\u2082(A) for any doubly stochastic matrix A (not necessarily symmetric), where \u03bb\u2082(A) is a nontrivial eigenvalue of A with maximum real part. Fiedler showed that the upper bound on \u03c6(A) is unaffected, i.e., \u03d5(A) \u2264 \u221a2\u22c5(1\u2212Re\u03bb\u2082(A)). With regards to the lower bound on \u03c6(A), there are known constructions with \u03d5(A) \u2208 \u0398(1\u2212Re\u03bb\u2082(A)/log n) indicating that at least a mild dependence on n is necessary to lower bound \u03c6(A). In our first result, we provide an exponentially better construction of n \u00d7 n doubly stochastic matrices A_n, for which \u03d5(An) \u2264 1\u2212Re\u03bb\u2082(A_n)/\u221an. In fact, all nontrivial eigenvalues of our matrices are 0, even though the matrices are highly nonexpanding. We further show that this bound is in the correct range (up to the exponent of n), by showing that for any doubly stochastic matrix A, \u03d5(A) \u2265 1\u2212Re\u03bb\u2082(A)/35\u22c5n As a consequence, unlike the symmetric case, there is a (necessary) loss of a factor of n^\u03b1 for \u00bd \u2264 \u03b1 \u2264 1 in lower bounding \u03c6 by the spectral gap in the nonsymmetric setting. Our second result extends these bounds to general matrices R with nonnegative entries, to obtain a two-sided gapped refinement of the Perron-Frobenius theorem. Recall from the Perron-Frobenius theorem that for such R, there is a nonnegative eigenvalue r such that all eigenvalues of R lie within the closed disk of radius r about 0. Further, if R is irreducible, which means \u03c6(R) > 0 (for suitably defined \u03c6), then r is positive and all other eigenvalues lie within the open disk, so (with eigenvalues sorted by real part), Re \u03bb\u2082(R) < r. An extension of Fiedler's result provides an upper bound and our result provides the corresponding lower bound on \u03c6(R) in terms of r \u2013 Re \u03bb\u2082(R), obtaining a two-sided quantitative version of the Perron-Frobenius theorem.", "date": "2020-01", "date_type": "published", "publisher": "Society for Industrial and Applied Mathematics", "place_of_pub": "Philadelphia, PA", "pagerange": "1200-1213", "id_number": "CaltechAUTHORS:20200828-114509192", "isbn": "978-1-61197-599-4", "book_title": "Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200828-114509192", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1319745" }, { "agency": "NSF", "grant_number": "CCF-1553477" }, { "agency": "NSF", "grant_number": "CCF-1618795" }, { "agency": "NSF", "grant_number": "CCF-1909972" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2012333" }, { "agency": "Israel Institute for Advanced Studies" }, { "agency": "EURIAS Senior Fellowship" }, { "agency": "Marie Curie Fellowship" } ] }, "doi": "10.1137/1.9781611975994.73", "primary_object": { "basename": "1.9781611975994.73.pdf", "url": "https://authors.library.caltech.edu/records/nmy3x-1w272/files/1.9781611975994.73.pdf" }, "related_objects": [ { "basename": "1909.12497.pdf", "url": "https://authors.library.caltech.edu/records/nmy3x-1w272/files/1909.12497.pdf" } ], "resource_type": "book_section", "pub_year": "2020", "author_list": "Mehta, Jenish C. and Schulman, Leonard J." }, { "id": "https://authors.library.caltech.edu/records/c1fyz-btw70", "eprint_id": 89095, "eprint_status": "archive", "datestamp": "2023-08-19 09:33:26", "lastmod": "2023-10-18 22:30:59", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Cohen-Gil", "name": { "family": "Cohen", "given": "Gil" } }, { "id": "Haeupler-B", "name": { "family": "Haeupler", "given": "Bernhard" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "Explicit binary tree codes with polylogarithmic size alphabet", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "tree codes, sparse polynomials, explicit constructions", "note": "\u00a9 2018 Association for Computing Machinery. \n\nPart of this work was done while the first author was a CMI Postdoctoral Fellow at the California Institute of Technology. The second author was supported in part by NSF grants CCF-1527110, CCF-1618280 and NSF CAREER award CCF-1750808. The third author was supported in part by NSF grant 1618795; and part of the work was done while he was in residence at the Israel Institute for Advanced Studies, supported by a EURIAS Senior Fellowship co-funded by the Marie Sk\u0142odowska-Curie Actions under the 7th Framework Programme. The second author thanks Noga Ron-Zewi and Shachar Lovett for many helpful discussions.", "abstract": "This paper makes progress on the problem of explicitly constructing a binary tree code with constant distance and constant alphabet size. \n\nWe give an explicit binary tree code with constant distance and alphabet size poly(logn), where n is the depth of the tree. This is the first improvement over a two-decade-old construction that has an exponentially larger alphabet of size poly(n). \n\nAt the core of our construction is the first explicit tree code with constant rate and constant distance, though with non-constant arity - a result of independent interest. This construction adapts the polynomial interpolation framework to the online setting.", "date": "2018-06", "date_type": "published", "publisher": "Association for Computing Machinery", "place_of_pub": "New York, NY", "pagerange": "535-544", "id_number": "CaltechAUTHORS:20180823-141633075", "isbn": "978-1-4503-5559-9", "book_title": "Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180823-141633075", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Center for the Mathematics of Information, Caltech" }, { "agency": "NSF", "grant_number": "CCF-1527110" }, { "agency": "NSF", "grant_number": "CCF-1618280" }, { "agency": "NSF", "grant_number": "CCF-1750808" }, { "agency": "NSF", "grant_number": "CCF-1618795" }, { "agency": "European Institutes for Advanced Study (EURIAS)" }, { "agency": "Marie Curie Fellowship" } ] }, "doi": "10.1145/3188745.3188928", "resource_type": "book_section", "pub_year": "2018", "author_list": "Cohen, Gil; Haeupler, Bernhard; et el." }, { "id": "https://authors.library.caltech.edu/records/x2458-79e56", "eprint_id": 85735, "eprint_status": "archive", "datestamp": "2023-08-19 07:11:31", "lastmod": "2023-10-18 18:43:55", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kempe-D", "name": { "family": "Kempe", "given": "David" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Quasi-regular sequences and optimal schedules for security games", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2018 SIAM. \n\nSupported in parts by NSF grants 1619458 and 1423618. \n\nSupported in part by NSF grants 1319745, 1618795, and a EURIAS Senior Fellowship co-funded by the Marie Sk\u0142odowska-Curie Actions under the 7th Framework Programme. \n\nThis work was supported by a grant from the Simons Foundation (#419427, Omer Tamuz).\n\nPublished - p1625-kempe.pdf

Submitted - 1611.07169.pdf

", "abstract": "We study security games in which a defender commits to a mixed strategy for protecting a finite set of targets of different values. An attacker, knowing the defender's strategy, chooses which target to attack and for how long. If the attacker spends time t at a target i of value \u03b1_i, and if he leaves before the defender visits the target, his utility is t \u00b7 \u03b1_i; if the defender visits before he leaves, his utility is 0. The defender's goal is to minimize the attacker's utility. The defender's strategy consists of a schedule for visiting the targets; it takes her unit time to switch between targets. Such games are a simplified model of a number of real-world scenarios such as protecting computer networks from intruders, crops from thieves, etc.\n\nWe show that optimal defender play for such security games, although played in continuous time, reduces to the solution of a combinatorial question regarding the existence of infinite sequences over a finite alphabet, with the following properties for each symbol i: (1) i constitutes a prescribed limiting fraction p_i of the sequence. (2) The occurrences of i are spread apart close to evenly, in that the ratio of the longest to shortest interval between consecutive occurrences is bounded by a parameter K. We call such sequences K-quasi-regular; a 1-quasi-regular sequence is one in which the occurrences of each symbol form an arithmetic sequence. \n\nAs we show, a 1-quasi-regular sequence ensures an optimal defender strategy for these security games: the intuition for this fact lies in the famous \"inspection paradox.\" However, as we demonstrate, for K < 2 and general p_i, K-quasi-regular sequences may not exist. Fortunately, this does not turn out to be an obstruction: we show that, surprisingly, 2-quasi-regular sequences also suffice for optimal defender play. What is more, even randomized 2-quasi-regular sequences suffice for optimality. We show that such sequences always exist, and can be calculated efficiently. Thus, we can ensure optimal defender play for these security games. \n\nThe question of the least K for which deterministic K-quasi-regular sequences exist is fascinating. Using an ergodic theoretical approach, we proceed to show that deterministic 3-quasi-regular sequences always exist (and can be calculated efficiently). We also show that these deterministic 3-regular sequences give rise to a \u2248 1.006-approximation algorithm for the defender's optimal strategy. For 2 \u2264 K < 3 we do not know whether deterministic K-quasi-regular sequences always exist; however, when the pi are all small, improved bounds are possible, and in fact, (1 + \u220a)-quasi-regular deterministic sequences exist for any \u220a > 0 for sufficiently small p_i.", "date": "2018-01", "date_type": "published", "publisher": "Society for Industrial and Applied Mathematics", "place_of_pub": "Philadelphia, PA", "pagerange": "1625-1644", "id_number": "CaltechAUTHORS:20180410-145958889", "isbn": "978-1-6119-7503-1", "book_title": "Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180410-145958889", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1619458" }, { "agency": "NSF", "grant_number": "DMS-1423618" }, { "agency": "NSF", "grant_number": "DMS-1319745" }, { "agency": "NSF", "grant_number": "DMS-1618795" }, { "agency": "Marie Curie Fellowship" }, { "agency": "Simons Foundation", "grant_number": "419427" } ] }, "contributors": { "items": [ { "id": "Czumaj-A", "name": { "family": "Czumaj", "given": "Artur" } } ] }, "doi": "10.1137/1.9781611975031.106", "primary_object": { "basename": "1611.07169.pdf", "url": "https://authors.library.caltech.edu/records/x2458-79e56/files/1611.07169.pdf" }, "related_objects": [ { "basename": "p1625-kempe.pdf", "url": "https://authors.library.caltech.edu/records/x2458-79e56/files/p1625-kempe.pdf" } ], "resource_type": "book_section", "pub_year": "2018", "author_list": "Kempe, David; Schulman, Leonard J.; et el." }, { "id": "https://authors.library.caltech.edu/records/b9z6j-aqc54", "eprint_id": 74305, "eprint_status": "archive", "datestamp": "2023-08-19 00:49:46", "lastmod": "2023-10-24 22:27:50", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dvijotham-Krishnamurthy", "name": { "family": "Dvijotham", "given": "Krishnamurthy" }, "orcid": "0000-0002-1328-4677" }, { "id": "Rabani-Yuval", "name": { "family": "Rabani", "given": "Yuval" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "Convergence of Incentive-Driven Dynamics in Fisher Markets", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2017 SIAM. \n\n[YR] supported in part by ISF grant 956-15, BSF grant 2012333 and I-CORE Algo. \n\n[LJS] supported in part by NSF grants 1319745, 1618795, and BSF grant 2012333.\n\nPublished - 1_2E9781611974782_2E35.pdf

", "abstract": "In both general equilibrium theory and game theory, the dominant mathematical models rest on a fully rational solution concept in which every player's action is a best-response to the actions of the other players. In both theories there is less agreement on suitable out- of-equilibrium modeling, but one attractive approach is the level k model in which a level 0 player adopts a very simple response to current conditions, a level 1 player best-responds to a model in which others take level 0 actions, and so forth. (This is analogous to k-ply exploration of game trees in AI, and to receding-horizon control in control theory.) If players have deterministic mental models with this kind of finite-level response, there is obviously no way their mental models can all be consistent. Nevertheless, there is experimental evidence that people act this way in many situations, motivating the question of what the dynamics of such interactions lead to.\n\nWe address the problem of out-of-equilibrium price dynamics in the setting of Fisher markets. We develop a general framework in which sellers have (a) a set of atomic price update rules which are simple responses to a price vector; (b) a belief-formation procedure that simulates actions of other sellers (themselves using the atomic price updates) to some finite horizon in the future. In this framework, sellers use an atomic price update rule to respond to a price vector they generate with the belief formation procedure. The framework is general and allows sellers to have inconsistent and time- varying beliefs about each other. Under certain assumptions on the atomic update rules, we show that despite the inconsistent and time-varying nature of beliefs, the market converges to a unique equilibrium. (If the price updates are driven by weak-gross substitutes demands, this is the same equilibrium point predicted by those demands.) This result holds for both synchronous and asynchronous discrete-time updates. Moreover, the result is computationally feasible in the sense that the convergence rate is linear, i.e., the distance to equilibrium decays exponentially fast. To the best of our knowledge, this is the first result that demonstrates, in Fisher markets, convergence at any rate for dynamics driven by a plausible model of seller incentives.\n\nWe then specialize our results to Fisher markets with elastic demands (a further special case corresponds to demand generated by buyers with constant elasticity of substitution (CES) utilities, in the weak gross substitutes (WGS) regime) and show that the atomic update rule in which a seller uses the best-response (=profit- maximizing) update given the prices of all other sellers, satisfies the assumptions required on atomic price update rules in our framework. We can even characterize the convergence rate (as a function of elasticity parameters of the demand function).\n\nOur results apply also to settings where, to the best of our knowledge, there exists no previous demonstration of efficient convergence of any discrete dynamic of price updates. Even for the simple case of (level 0) best- response dynamics, our result is the first to demonstrate a linear rate of convergence.", "date": "2017-01", "date_type": "published", "publisher": "SIAM", "place_of_pub": "Philadelphia, PA", "pagerange": "554-567", "id_number": "CaltechAUTHORS:20170214-145943460", "isbn": "978-1-61197-478-2", "book_title": "Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170214-145943460", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Israel Science Foundation", "grant_number": "956-15" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2012333" }, { "agency": "Israeli Centers for Research Excellence (I-CORE)" }, { "agency": "NSF", "grant_number": "CCF-1319745" }, { "agency": "NSF", "grant_number": "CCF-1618795" } ] }, "collection": "CaltechAUTHORS", "doi": "10.1137/1.9781611974782.35", "primary_object": { "basename": "1_2E9781611974782_2E35.pdf", "url": "https://authors.library.caltech.edu/records/b9z6j-aqc54/files/1_2E9781611974782_2E35.pdf" }, "resource_type": "book_section", "pub_year": "2017", "author_list": "Dvijotham, Krishnamurthy; Rabani, Yuval; et el." }, { "id": "https://authors.library.caltech.edu/records/2s0v3-paf71", "eprint_id": 94377, "eprint_status": "archive", "datestamp": "2023-08-19 00:54:45", "lastmod": "2024-01-14 21:41:33", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" }, { "id": "Vazirani-Umesh-V", "name": { "family": "Vazirani", "given": "Umesh V." } } ] }, "title": "The duality gap for two-team zero-sum games", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2017 Leonard Schulman and Umesh Vazirani; licensed under Creative Commons License CC-BY. \n\nLJS was supported in part by NSF grants 1319745/1618795 and BSF grant 2012333; UVV was supported in part by NSF Grant CCF-1410022.\n\nPublished - LIPIcs-ITCS-2017-56.pdf

", "abstract": "We consider multiplayer games in which the players fall in two teams of size k, with payoffs equal within, and of opposite sign across, the two teams. In the classical case of k = 1, such zero-sum games possess a unique value, independent of order of play, due to the von Neumann minimax\ntheorem. However, this fails for all k > 1; we can measure this failure by a duality gap, which quantifies the benefit of being the team to commit last to its strategy. In our main result we show that the gap equals 2(1 \u2013 2^(1\u2212k)) for m = 2 and 2(1 \u2013 m^(\u2212(1\u2212o(1))k)) for m > 2, with m being the\nsize of the action space of each player. At a finer level, the cost to a team of individual players acting independently while the opposition employs joint randomness is 1 \u2013 2^(1\u2212k) for k = 2, and 1 \u2013 m^(\u2212(1\u2212o(1))k) for m > 2.\nThis class of multiplayer games, apart from being a natural bridge between two-player zero-sum games and general multiplayer games, is motivated from Biology (the weak selection model of evolution) and Economics (players with shared utility but poor coordination).", "date": "2017-01", "date_type": "published", "publisher": "Dagstuhl Publishing", "place_of_pub": "Saarbr\u00fccken, Germany", "pagerange": "Art. No. 56", "id_number": "CaltechAUTHORS:20190402-143205523", "isbn": "978-3-95977-029-3", "book_title": "8th Innovations in Theoretical Computer Science Conference", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190402-143205523", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1319745" }, { "agency": "NSF", "grant_number": "CCF-1618795" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2012333" }, { "agency": "NSF", "grant_number": "CCF-1410022" } ] }, "contributors": { "items": [ { "id": "Papadimitrou-Christos-H", "name": { "family": "Papadimitrou", "given": "Christos H." } } ] }, "doi": "10.4230/LIPIcs.ITCS.2017.56", "primary_object": { "basename": "LIPIcs-ITCS-2017-56.pdf", "url": "https://authors.library.caltech.edu/records/2s0v3-paf71/files/LIPIcs-ITCS-2017-56.pdf" }, "resource_type": "book_section", "pub_year": "2017", "author_list": "Schulman, Leonard J. and Vazirani, Umesh V." }, { "id": "https://authors.library.caltech.edu/records/bs3ee-mwm86", "eprint_id": 73784, "eprint_status": "archive", "datestamp": "2023-08-20 14:04:40", "lastmod": "2023-10-24 16:27:01", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Cohen-Gil", "name": { "family": "Cohen", "given": "Gil" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "Extractors for Near Logarithmic Min-Entropy", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2016 IEEE.", "abstract": "The main contribution of this work is an explicit construction of extractors for near logarithmic min-entropy. For any \u03b4 > 0 we construct an extractor for O(1/\u03b4) n-bit sources with min-entropy (logn)^(1+\u03b4). This is most interesting when \u03b4 is set to a small constant, though the result also yields an extractor for O(log logn) sources with logarithmic min-entropy. Prior to this work, the best explicit extractor in terms of supporting least-possible min-entropy, due to Li (FOCS'15), requires min-entropy (logn)^(2+\u03b4) from its O(1/\u03b4) sources. Further, all current techniques for constructing multi-source extractors \"break\" below min-entropy (log n)^2. In fact, existing techniques do not provide even a disperser for o(log n) sources each with min-entropy (log n)^(1.99). Apart from being a natural problem, supporting logarithmic min-entropy has applications to combinatorics. A two-source disperser, let alone an extractor, for min-entropy O(log n) induces a (log, nO(1))-Ramsey graph on n vertices. Thus, constructing such dispersers would be a significant step towards constructively matching Erd\u00f6s' proof for the existence of (2log n)-Ramsey graphs on n vertices. Our construction does not rely on the sophisticated primitives that were key to the substantial recent progress on multi-source extractors, such as non-malleable extractors, correlation breakers, the lightest-bin condenser, or extractors for non-oblivious bit-fixing sources, although some of these primitives can be combined with our construction so to improve the output length and the error guarantee. Instead, at the heart of our construction is a new primitive called an independence-preserving merger. The construction of the latter builds on the alternating extraction technique.", "date": "2016-10", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "178-187", "id_number": "CaltechAUTHORS:20170127-140321585", "isbn": "978-1-5090-3933-3", "book_title": "IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170127-140321585", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1109/FOCS.2016.27", "resource_type": "book_section", "pub_year": "2016", "author_list": "Cohen, Gil and Schulman, Leonard J." }, { "id": "https://authors.library.caltech.edu/records/n90z2-k3643", "eprint_id": 68719, "eprint_status": "archive", "datestamp": "2023-08-20 11:50:43", "lastmod": "2023-10-19 23:34:27", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" }, { "id": "Srivastava-P", "name": { "family": "Srivastava", "given": "Piyush" }, "orcid": "0000-0003-0953-2890" } ] }, "title": "Stability of Causal Inference", "ispublished": "unpub", "full_text_status": "public", "note": "This research was supported by NSF grant CCF-1319745.\nWe thank the reviewers for helpful comments.\n\nPublished - 214.pdf

", "abstract": "We consider the sensitivity of causal identification\nto small perturbations in the input. A long line of\nwork culminating in papers by Shpitser and Pearl\n(2006) and Huang and Valtorta (2008) led to a\ncomplete procedure for the causal identification\nproblem. In our main result in this paper, we\nshow that the identification function computed\nby these procedures is in some cases extremely\nunstable numerically. Specifically, the \"condition\nnumber\" of causal identification can be of the\norder of \u03a9(exp(n\n^(0.49))) on an identifiable semiMarkovian\nmodel with n visible nodes. That is,\nin order to give an output accurate to d bits, the\nempirical probabilities of the observable events\nneed to be obtained to accuracy d + \u03a9(n\n^(0.49)) bits.", "date": "2016-06", "date_type": "published", "publisher": "Caltech Library", "id_number": "CaltechAUTHORS:20160628-152001110", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160628-152001110", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1319745" } ] }, "primary_object": { "basename": "214.pdf", "url": "https://authors.library.caltech.edu/records/n90z2-k3643/files/214.pdf" }, "resource_type": "book_section", "pub_year": "2016", "author_list": "Schulman, Leonard J. and Srivastava, Piyush" }, { "id": "https://authors.library.caltech.edu/records/77mce-h7v87", "eprint_id": 65380, "eprint_status": "archive", "datestamp": "2023-08-20 09:45:14", "lastmod": "2023-10-18 15:57:40", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hoza-W-M", "name": { "family": "Hoza", "given": "William M." } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "The adversarial noise threshold for distributed protocols", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2016 SIAM. \n\nSupported by a Nellie Bergen and Adrian Foster Tillotson Summer Undergraduate Research Fellowship from the California Institute of Technology, as well as by the ARCS Los Angeles Founder Chapter. \n\nSupported in part by NSF Award 1319745. \n\nWe thank anonymous reviewers for numerous suggestions, including the observation that Theorems 6 and 7 extend to large alphabets.\n\nPublished - p240-hoza.pdf

Submitted - 1412.8097v2.pdf

", "abstract": "We consider the problem of implementing distributed protocols, despite adversarial channel errors, on synchronous-messaging networks with arbitrary topology. \n\nIn our first result we show that any n-party T-round protocol on an undirected communication network G can be compiled into a robust simulation protocol on a sparse (O(n) edges) subnetwork so that the simulation tolerates an adversarial error rate of \u03a9(1n); the simulation has a round complexity of O(m log n/nT), where m is the number of edges in G. (So the simulation is work-preserving up to a log factor.) The adversary's error rate is within a constant factor of optimal. Given the error rate, the round complexity blowup is within a factor of O(k log n) of optimal, where k is the edge connectivity of G. We also determine that the maximum tolerable error rate on directed communication networks is \u0398(1/s) where s is the number of edges in a minimum equivalent digraph. \nNext we investigate adversarial per-edge error rates, where the adversary is given an error budget on each edge of the network. We determine the exact limit for tolerable per-edge error rates on an arbitrary directed graph. However, the construction that approaches this limit has exponential round complexity, so we give another compiler, which transforms T-round protocols into O(mT)-round simulations, and prove that for polynomial-query black box compilers, the per-edge error rate tolerated by this last compiler is within a constant factor of optimal.", "date": "2016-01", "date_type": "published", "publisher": "Association for Computing Machinery", "place_of_pub": "New York, NY", "pagerange": "240-258", "id_number": "CaltechAUTHORS:20160316-071949447", "isbn": "978-1-611974-33-1", "book_title": "Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160316-071949447", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" }, { "agency": "ARCS Los Angeles Founder Chapter" }, { "agency": "NSF", "grant_number": "1319745" } ] }, "doi": "10.48550/arXiv.1412.8097", "primary_object": { "basename": "1412.8097v2.pdf", "url": "https://authors.library.caltech.edu/records/77mce-h7v87/files/1412.8097v2.pdf" }, "related_objects": [ { "basename": "p240-hoza.pdf", "url": "https://authors.library.caltech.edu/records/77mce-h7v87/files/p240-hoza.pdf" } ], "resource_type": "book_section", "pub_year": "2016", "author_list": "Hoza, William M. and Schulman, Leonard J." }, { "id": "https://authors.library.caltech.edu/records/js85e-0ah54", "eprint_id": 69443, "eprint_status": "archive", "datestamp": "2023-08-22 16:28:08", "lastmod": "2024-01-13 16:53:04", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" }, { "id": "Sinclair-A", "name": { "family": "Sinclair", "given": "Alistair" } }, { "id": "Srivastava-P", "name": { "family": "Srivastava", "given": "Piyush" }, "orcid": "0000-0003-0953-2890" } ] }, "title": "Symbolic Integration and the Complexity of Computing Averages", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Computational Complexity; Statistical Mechanics; Counting Problems; #P-hardness", "note": "\u00a9 2015 IEEE. \n\nWe thank an anonymous referee for observing that an appeal to the polynomial factoring algorithm of Lenstra, Lenstra and Lov\u00e1sz is not necessary in the proof of our main technical lemma. \n\nLJS and PS were supported in part by NSF grant CCF-1319745. AS was supported by in part by NSF grant CCF-1420934 and the Simons Institute for the Theory of Computing.", "abstract": "We study the computational complexity of several natural problems arising in statistical physics and combinatorics. In particular, we consider the following problems: the mean magnetization and mean energy of the Ising model (both the ferromagnetic and the anti-ferromagnetic settings), the average size of an independent set in the hard core model, and the average size of a matching in the monomer-dimer model. We prove that for all non-trivial values of the underlying model parameters, exactly computing these averages is #P-hard. \n\nIn contrast to previous results of Sinclair and Srivastava [1] for the mean magnetization of the ferromagnetic Ising model, our approach does not use any Lee-Yang type theorems about the complex zeros of partition functions. Indeed, it was due to the lack of suitable Lee-Yang theorems for models such as the anti-ferromagnetic Ising model that some of the problems we study here were left open in [1]. In this paper, we instead use some relatively simple and well-known ideas from the theory of automatic symbolic integration to complete our hardness reductions.", "date": "2015-10", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "1231-1245", "id_number": "CaltechAUTHORS:20160804-113612809", "isbn": "978-1-4673-8191-8", "book_title": "IEEE 56th Annual Symposium on Foundations of Computer Science", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160804-113612809", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1319745" }, { "agency": "NSF", "grant_number": "CCF-1420934" }, { "agency": "Simons Institute for the Theory of Computing" } ] }, "doi": "10.1109/FOCS.2015.79", "resource_type": "book_section", "pub_year": "2015", "author_list": "Schulman, Leonard J.; Sinclair, Alistair; et el." }, { "id": "https://authors.library.caltech.edu/records/45nqa-2ev81", "eprint_id": 58889, "eprint_status": "archive", "datestamp": "2023-08-20 06:28:31", "lastmod": "2023-10-23 19:50:54", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" }, { "id": "Sinclair-A", "name": { "family": "Sinclair", "given": "Alistair" } } ] }, "title": "Analysis of a Classical Matrix Preconditioning Algorithm", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2015 ACM.\n\nWork supported in part by NSF grants 1038578 and 1319745 and by the Simons Institute for the Theory of Computing, where some of this work was performed.\n\nWork supported in part by NSF grants 1016896 and 1420934.\n\nWe thank Tzu-Yi Chen and Jim Demmel for introducing us to this problem and for several helpful pointers, Martin Dyer for useful discussions, and Yuval Rabani for help in the early stages of this work which led to the proof of Theorem 1. We also thank anonymous referees of an earlier version for suggestions that improved the presentation of the paper.\n\nSubmitted - 1504.03026v2.pdf

", "abstract": "We study a classical iterative algorithm for the problem of balancing matrices in the L\u221e norm via a scaling transformation. This algorithm, which goes back to Osborne and Parlett & Reinsch in the 1960s, is implemented as a standard preconditioner in many numerical linear algebra packages. Surprisingly, despite its widespread use over several decades, no bounds were known on its rate of convergence. In this paper we prove that, for a large class of irreducible n x n (real or complex) input matrices A, a natural variant of the algorithm converges in O(n^3 log(n\u03c1/\u03b5)) elementary balancing operations, where \u03c1 measures the initial imbalance of A and \u03b5 is the target imbalance of the output matrix. (The imbalance of A is maxi |log(a_i^(out)/a_i^(in))|, where a_i^(out),a_i^(in) are the maximum entries in magnitude in the ith row and column respectively.) This bound is tight up to the log n factor. A balancing operation scales the ith row and column so that their maximum entries are equal, and requires O(m/n) arithmetic operations on average, where m is the number of non-zero elements in A. Thus the running time of the iterative algorithm is ~O(n^2m). This is the first time bound of any kind on any variant of the Osborne-Parlett-Reinsch algorithm. The class of matrices for which the above analysis holds are those which satisfy a condition we call Unique Balance, meaning that the limit of the iterative balancing process does not depend on the order in which balancing operations are performed. We also prove a combinatorial characterization of the Unique Balance property, which had earlier been conjectured by Chen.", "date": "2015-06", "date_type": "published", "publisher": "Association for Computing Machinery", "place_of_pub": "New York, NY", "pagerange": "831-840", "id_number": "CaltechAUTHORS:20150715-085040447", "isbn": "978-1-4503-3536-2", "book_title": "Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150715-085040447", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "1038578" }, { "agency": "NSF", "grant_number": "1319745" }, { "agency": "Simons Institute for the Theory of Computing" }, { "agency": "NSF", "grant_number": "1016896" }, { "agency": "NSF", "grant_number": "1420934" } ] }, "doi": "10.1145/2746539.2746556", "primary_object": { "basename": "1504.03026v2.pdf", "url": "https://authors.library.caltech.edu/records/45nqa-2ev81/files/1504.03026v2.pdf" }, "resource_type": "book_section", "pub_year": "2015", "author_list": "Schulman, Leonard J. and Sinclair, Alistair" }, { "id": "https://authors.library.caltech.edu/records/97whm-jn174", "eprint_id": 58890, "eprint_status": "archive", "datestamp": "2023-08-20 06:28:40", "lastmod": "2023-10-23 19:51:00", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Li-Jian", "name": { "family": "Li", "given": "Jian" }, "orcid": "0000-0003-0297-6528" }, { "id": "Rabani-Y", "name": { "family": "Rabani", "given": "Yuval" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" }, { "id": "Swamy-C", "name": { "family": "Swamy", "given": "Chaitanya" } } ] }, "title": "Learning Arbitrary Statistical Mixtures of Discrete Distributions", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2015 ACM.\n\nSupported in part by the National Basic Research Program of China grants 2015CB358700, 2011CBA00300, 2011CBA00301, and the National NSFC grants 61202009, 61033001, 61361136003. Work performed in part at the Simons Institute for the Theory of Computing.\n\nSupported by BSF grant number 2012333, and by the Israeli Center of Excellence on Algorithms.\n\nSupported in part by NSF grant 1319745. Work performed in part at the Simons Institute for the Theory of Computing.\n\nSupported in part by NSERC grant 32760-06, an NSERC Discovery Accelerator Supplement Award, and an Ontario Early Researcher Award.\n\nSubmitted - 1504.02526v1.pdf

", "abstract": "We study the problem of learning from unlabeled samples very general statistical mixture models on large finite sets. Specifically, the model to be learned, mix, is a probability distribution over probability distributions p, where each such p is a probability distribution over [n] = {1,2,...,n}. When we sample from mix, we do not observe p directly, but only indirectly and in very noisy fashion, by sampling from [n] repeatedly, independently K times from the distribution p. The problem is to infer mix to high accuracy in transportation (earthmover) distance.\nWe give the first efficient algorithms for learning this mixture model without making any restricting assumptions on the structure of the distribution mix. We bound the quality of the solution as a function of the size of the samples K and the number of samples used. Our model and results have applications to a variety of unsupervised learning scenarios, including learning topic models and collaborative filtering.", "date": "2015-06", "date_type": "published", "publisher": "Association for Computing Machinery", "place_of_pub": "New York, NY", "pagerange": "743-752", "id_number": "CaltechAUTHORS:20150715-085732981", "isbn": "978-1-4503-3536-2", "book_title": "Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150715-085732981", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "National Basic Research Program of China", "grant_number": "2015CB358700" }, { "agency": "National Basic Research Program of China", "grant_number": "2011CBA00300" }, { "agency": "National Basie Research Program of China", "grant_number": "2011CBA00301" }, { "agency": "National Science Foundation of China (NSFC)", "grant_number": "61202009" }, { "agency": "National Science Foundation of China (NSFC)", "grant_number": "61033001" }, { "agency": "National Science Foundation of China (NSFC)", "grant_number": "61361136003" }, { "agency": "Simons Institute for the Theory of Computing" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2012333" }, { "agency": "Israeli Center of Excellence on Algorithms" }, { "agency": "NSF", "grant_number": "1319745" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "32760-06" }, { "agency": "Ontario Early Researcher Award" } ] }, "doi": "10.1145/2746539.2746584", "primary_object": { "basename": "1504.02526v1.pdf", "url": "https://authors.library.caltech.edu/records/97whm-jn174/files/1504.02526v1.pdf" }, "resource_type": "book_section", "pub_year": "2015", "author_list": "Li, Jian; Rabani, Yuval; et el." }, { "id": "https://authors.library.caltech.edu/records/4char-3ct96", "eprint_id": 63366, "eprint_status": "archive", "datestamp": "2023-08-22 13:50:24", "lastmod": "2023-10-25 23:45:49", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bhaskar-U", "name": { "family": "Bhaskar", "given": "Umang" } }, { "id": "Ligett-K", "name": { "family": "Ligett", "given": "Katrina" }, "orcid": "0000-0003-2780-6656" }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" }, { "id": "Swamy-Chaitanya", "name": { "family": "Swamy", "given": "Chaitanya" } } ] }, "title": "Achieving Target Equilibria in Network Routing Games without Knowing the Latency Functions", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Network routing; tolls; ellipsoid method; approximate equilibria; multicommodity flows; Stackelberg routing", "note": "\u00a9 2014 IEEE. \n\nWe thank \u00c9va Tardos for useful discussions. UB was supported by a Linde/SISL postdoctoral fellowship and NSF grants CNS-0846025, CCF-1101470 and EPAS-1307794. KL was supported by the Charles Lee Powell Foundation and a Microsoft Faculty Fellowship. LJS was supported by NSF grants 1038578 and 1319745, and was partly at the Simons Institute at UC Berkeley. CS was supported by NSERC grant 32760-06, an NSERC Discovery Accelerator Supplement Award, and an Ontario Early Researcher Award.", "abstract": "The analysis of network routing games typically assumes, right at the onset, precise and detailed information about the latency functions. Such information may, however, be unavailable or difficult to obtain. Moreover, one is often primarily interested in enforcing a desirable target flow as the equilibrium by suitably influencing player behavior in the routing game. We ask whether one can achieve target flows as equilibria without knowing the underlying latency functions. Our main result gives a crisp positive answer to this question. We show that, under fairly general settings, one can efficiently compute edge tolls that induce a given target multicommodity flow in a nonatomic routing game using a polynomial number of queries to an oracle that takes candidate tolls as input and returns the resulting equilibrium flow. This result is obtained via a novel application of the ellipsoid method, and applies to arbitrary multicommodity settings and non-linear latency functions. Our algorithm extends easily to many other settings, such as (i) when certain edges cannot be tolled or there is an upper bound on the total toll paid by a user, and (ii) general nonatomic congestion games. We obtain tighter bounds on the query complexity for series-parallel networks, and single-commodity routing games with linear latency functions, and complement these with a query-complexity lower bound applicable even to single-commodity routing games on parallel-link graphs with linear latency functions. We also explore the use of Stackelberg routing to achieve target equilibria and obtain strong positive results for series-parallel graphs. Our results build upon various new techniques that we develop pertaining to the computation of, and connections between, different notions of approximate equilibrium, properties of multicommodity flows and tolls in series-parallel graphs, and sensitivity of equilibrium flow with respect to tolls. Our results demonstrate that one can indeed circumvent the potentially-onerous task of modeling latency functions, and yet obtain meaningful results for the underlying routing game.", "date": "2014-10", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "31-40", "id_number": "CaltechAUTHORS:20160105-073143688", "isbn": "978-1-4799-6517-5", "book_title": "IEEE 55th Annual Symposium on Foundations of Computer Science", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160105-073143688", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Linde Institute of Economic and Management Science" }, { "agency": "NSF", "grant_number": "CNS-0846025" }, { "agency": "NSF", "grant_number": "CCF-1101470" }, { "agency": "NSF", "grant_number": "EPAS-1307794" }, { "agency": "Charles Lee Powell Foundation" }, { "agency": "Microsoft Research Faculty Fellowship" }, { "agency": "NSF", "grant_number": "CCF-1038578" }, { "agency": "NSF", "grant_number": "CCF-1319745" }, { "agency": "University of California, Berkeley" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "32760-06" }, { "agency": "Ontario Early Researcher Award" }, { "agency": "Caltech Social and Information Sciences Laboratory" } ] }, "doi": "10.1109/FOCS.2014.12", "resource_type": "book_section", "pub_year": "2014", "author_list": "Bhaskar, Umang; Ligett, Katrina; et el." }, { "id": "https://authors.library.caltech.edu/records/jtczr-4n629", "eprint_id": 72750, "eprint_status": "archive", "datestamp": "2023-08-22 11:20:38", "lastmod": "2023-10-23 22:54:40", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rabani-Y", "name": { "family": "Rabani", "given": "Yuval" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" }, { "id": "Swamy-C", "name": { "family": "Swamy", "given": "Chaitanya" } } ] }, "title": "Learning mixtures of arbitrary distributions over large discrete domains", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Randomized algorithms; mixture learning; topic models; spectral techniques; moment methods; linear programming; convex geometry", "note": "\u00a9 2014 ACM. \n\nSupported in part by NSF CCF-1038578, NSF CCF-0515342, NSA H98230-06-1-0074, and NSF ITR CCR-0326554. \n\nSupported in part by NSERC grant 32760-06, an NSERC Discovery Accelerator Supplement Award, and an Ontario Early Researcher Award.", "abstract": "We give an algorithm for learning a mixture of unstructured distributions. This problem arises in various unsupervised learning scenarios, for example in learning topic models from a corpus of documents spanning several topics. We show how to learn the constituents of a mixture of k arbitrary distributions over a large discrete domain [n]={1, 2, ...,n} and the mixture weights, using O(n polylog n) samples. (In the topic-model learning setting, the mixture constituents correspond to the topic distributions.) \n\nThis task is information-theoretically impossible for k > 1 under the usual sampling process from a mixture distribution. However, there are situations (such as the above-mentioned topic model case) in which each sample point consists of several observations from the same mixture constituent. This number of observations, which we call the \"sampling aperture\", is a crucial parameter of the problem. \n\nWe obtain the first bounds for this mixture-learning problem without imposing any assumptions on the mixture constituents. We show that efficient learning is possible exactly at the information-theoretically least-possible aperture of 2k-1. Thus, we achieve near-optimal dependence on n and optimal aperture. While the sample-size required by our algorithm depends exponentially on k, we prove that such a dependence is unavoidable when one considers general mixtures. \n\nA sequence of tools contribute to the algorithm, such as concentration results for random matrices, dimension reduction, moment estimations, and sensitivity analysis.", "date": "2014-01", "date_type": "published", "publisher": "ACM", "place_of_pub": "New York, NY", "pagerange": "207-224", "id_number": "CaltechAUTHORS:20161212-165501273", "isbn": "978-1-4503-2698-8", "book_title": "ITCS '14 Proceedings of the 5th conference on Innovations in theoretical computer science", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161212-165501273", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1038578" }, { "agency": "NSF", "grant_number": "CCF-0515342" }, { "agency": "National Security Agency (NSA)", "grant_number": "H98230-06-1-0074" }, { "agency": "NSF", "grant_number": "ITR CCR-0326554" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "32760-06" }, { "agency": "Ontario Early Researcher Award" } ] }, "contributors": { "items": [ { "id": "Naor-M", "name": { "family": "Naor", "given": "Moni" } } ] }, "doi": "10.1145/2554797.2554818", "resource_type": "book_section", "pub_year": "2014", "author_list": "Rabani, Yuval; Schulman, Leonard J.; et el." }, { "id": "https://authors.library.caltech.edu/records/vh65c-pd908", "eprint_id": 44557, "eprint_status": "archive", "datestamp": "2023-08-22 11:18:28", "lastmod": "2023-10-26 14:46:58", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Moore-C", "name": { "family": "Moore", "given": "Cristopher" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "Tree Codes and a Conjecture on Exponential Sums", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Interactive communication; error-correcting codes; exponential sums", "note": "Copyright is held by the owner/author(s). Publication rights licensed to ACM.\n\nC.M. is supported by NSF grants CCF-1117426 and CCF-\n1219117, and ARO contract W911NF-04-R-0009. L.J.S. is\nsupported by NSF grant CCF-1038578. Many students'\nbranch and bound implementations were very successful (23\nstudents crossed the \u2113 = 100 threshold); we thank all for\ntheir dedication and enthusiasm. Specific results are cited\nwith permission. We also thank Alex Russell and Anup Rao\nfor helpful discussions.", "abstract": "We propose a new conjecture on some exponential sums.\nThese particular sums have not apparently been considered\nin the literature. Subject to the conjecture we obtain the\nfirst effective construction of asymptotically good tree codes.\nThe available numerical evidence is consistent with the conjecture and is sufficient to certify codes for significant-length communications.", "date": "2014-01", "date_type": "published", "publisher": "ACM", "place_of_pub": "New York, NY", "pagerange": "145-154", "id_number": "CaltechAUTHORS:20140331-152623727", "isbn": "978-1-4503-2698-8", "book_title": "Proceedings of the 5th conference on Innovations in theoretical computer science", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140331-152623727", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1117426" }, { "agency": "NSF", "grant_number": "CCF-1219117" }, { "agency": "Army Research Office (ARO)", "grant_number": "W911NF-04-R-009" }, { "agency": "NSF", "grant_number": "CCF-1038578" } ] }, "contributors": { "items": [ { "id": "Naor-M", "name": { "family": "Naor", "given": "Moni" } } ] }, "doi": "10.1145/2554797.2554813", "resource_type": "book_section", "pub_year": "2014", "author_list": "Moore, Cristopher and Schulman, Leonard J." }, { "id": "https://authors.library.caltech.edu/records/59t3z-qw360", "eprint_id": 55095, "eprint_status": "archive", "datestamp": "2023-08-19 22:45:56", "lastmod": "2024-01-13 16:16:08", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bhaskar-U", "name": { "family": "Bhaskar", "given": "Umang" } }, { "id": "Ligett-K", "name": { "family": "Ligett", "given": "Katrina" }, "orcid": "0000-0003-2780-6656" }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "Network Improvement for Equilibrium Routing", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2014 Springer International Publishing Switzerland.\n\nSupported in part by NSF Awards 1038578 and 1319745, an NSF CAREER Award\n(1254169), the Charles Lee Powell Foundation, and a Microsoft Research Faculty\nFellowship.", "abstract": "In routing games, agents pick routes through a network to\nminimize their own delay. A primary concern for the network designer\nin routing games is the average agent delay at equilibrium. A number of\nmethods to control this average delay have received substantial attention,\nincluding network tolls, Stackelberg routing, and edge removal.\nA related approach with arguably greater practical relevance is that\nof making investments in improvements to the edges of the network, so\nthat, for a given investment budget, the average delay at equilibrium in\nthe improved network is minimized. This problem has received considerable\nattention in the literature on transportation research. We study\na model for this problem introduced in transportation research literature,\nand present both hardness results and algorithms that obtain tight\nperformance guarantees.\n\u2013 In general graphs, we show that a simple algorithm obtains a\n4/3-approximation for affine delay functions and an O(p/ log p)-\napproximation for polynomial delay functions of degree p. For affine\ndelays, we show that it is NP-hard to improve upon the 4/3 approximation.\n\u2013 Motivated by the practical relevance of the problem, we consider restricted\ntopologies to obtain better bounds. In series-parallel graphs,\nwe show that the problem is still NP-hard. However, we show that\nthere is an FPTAS in this case.\n\u2013 Finally, for graphs consisting of parallel paths, we show that an optimal\nallocation can be obtained in polynomial time.", "date": "2014", "date_type": "published", "publisher": "Springer", "place_of_pub": "Cham, Switzerland", "pagerange": "138-149", "id_number": "CaltechAUTHORS:20150223-101614687", "isbn": "978-3-319-07556-3", "book_title": "Integer Programming and Combinatorial Optimization", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150223-101614687", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "1038578" }, { "agency": "NSF", "grant_number": "1319745" }, { "agency": "NSF", "grant_number": "1254169" }, { "agency": "Charles Lee Powell Foundation" }, { "agency": "Microsoft Research Faculty Fellowship" } ] }, "contributors": { "items": [ { "id": "Lee-J", "name": { "family": "Lee", "given": "Jon" } }, { "id": "Vygen-J", "name": { "family": "Vygen", "given": "Jens" } } ] }, "resource_type": "book_section", "pub_year": "2014", "author_list": "Bhaskar, Umang; Ligett, Katrina; et el." }, { "id": "https://authors.library.caltech.edu/records/kqzsq-8jg40", "eprint_id": 77033, "eprint_status": "archive", "datestamp": "2023-08-19 20:59:02", "lastmod": "2024-01-13 20:27:22", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Franklin-M", "name": { "family": "Franklin", "given": "Matthew" } }, { "id": "Gelles-R", "name": { "family": "Gelles", "given": "Ran" } }, { "id": "Ostrovsky-R", "name": { "family": "Ostrovsky", "given": "Rafail" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "Optimal Coding for Streaming Authentication and Interactive Communication", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2013 International Association for Cryptologic Research.\n\nSupported in part by NSF grants 0830803, 09165174, 1065276, 1118126 and 1136174, US-Israel BSF grant 2008411, OKAWA Foundation Research Award, IBM Faculty Research Award, Xerox Faculty Research Award, B. John Garrick Foundation\nAward, Teradata Research Award, and Lockheed-Martin Corporation Research Award. This material is based upon work supported by the Defense Advanced Research Projects Agency through the U.S. Office of Naval Research under Contract\nN00014-11-1-0392. The views expressed are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S. Government. Supported in part by NSF Award 1038578.", "abstract": "Error correction and message authentication are well studied in the literature, and various efficient solutions have been suggested and analyzed. This is however not the case for data streams in which the message is very long, possibly infinite, and not known in advance to the sender. Trivial solutions for error-correcting and authenticating data streams either suffer from a long delay at the receiver's end or cannot perform well when the communication channel is noisy.\n\nIn this work we suggest a constant-rate error-correction scheme and an efficient authentication scheme for data streams over a noisy channel (one-way communication, no feedback) in the shared-randomness model. Our first scheme does not assume shared randomness and (non-efficiently) recovers a (1\u2009\u2212\u20092c)-fraction prefix of the stream sent so far, assuming the noise level is at most c\u2009<\u20091/2. The length of the recovered prefix is tight.\n\nTo be able to overcome the c\u2009=\u20091/2 barrier we relax the model and assume the parties pre-share a secret key. Under this assumption we show that for any given noise rate c\u2009<\u20091, there exists a scheme that correctly decodes a (1\u2009\u2212\u2009c)-fraction of the stream sent so far with high probability, and moreover, the scheme is efficient. Furthermore, if the noise rate exceeds c, the scheme aborts with high probability. We also show that no constant-rate authentication scheme recovers more than a (1\u2009\u2212\u2009c)-fraction of the stream sent so far with non-negligible probability, thus the relation between the noise rate and recoverable fraction of the stream is tight, and our scheme is optimal.\n\nOur techniques also apply to the task of interactive communication (two-way communication) over a noisy channel. In a recent paper, Braverman and Rao [STOC 2011] show that any function of two inputs has a constant-rate interactive protocol for two users that withstands a noise rate up to 1/4. By assuming that the parties share a secret random string, we extend this result and construct an interactive protocol that succeeds with overwhelming probability against noise rates up to 1/2. We also show that no constant-rate protocol exists for noise rates above 1/2 for functions that require two-way communication. This is contrasted with our first result in which computing the \"function\" requires only one-way communication and the noise rate can go up to 1.", "date": "2013-08", "date_type": "published", "publisher": "Springer", "place_of_pub": "Berlin", "pagerange": "258-276", "id_number": "CaltechAUTHORS:20170427-165048383", "isbn": "978-3-642-40083-4", "book_title": "Advances in Cryptology \u2013 CRYPTO 2013", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170427-165048383", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "0830803" }, { "agency": "NSF", "grant_number": "09165174" }, { "agency": "NSF", "grant_number": "1065276" }, { "agency": "NSF", "grant_number": "1118126" }, { "agency": "NSF", "grant_number": "1136174" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2008411" }, { "agency": "Okawa Foundation" }, { "agency": "IBM" }, { "agency": "Xerox" }, { "agency": "B. John Garrick Foundation" }, { "agency": "Teradata" }, { "agency": "Lockheed-Martin Corporation" }, { "agency": "Office of Naval Research (ONR)", "grant_number": "N00014-11-1-0392" }, { "agency": "NSF", "grant_number": "1038578" } ] }, "doi": "10.1007/978-3-642-40084-1_15", "resource_type": "book_section", "pub_year": "2013", "author_list": "Franklin, Matthew; Gelles, Ran; et el." }, { "id": "https://authors.library.caltech.edu/records/33twp-b8r58", "eprint_id": 72226, "eprint_status": "archive", "datestamp": "2023-08-19 14:15:07", "lastmod": "2023-10-23 20:31:43", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Lee-Euiwoong", "name": { "family": "Lee", "given": "Euiwoong" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "Clustering affine subspaces: hardness and algorithms", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2013 SIAM. \n\nSupported in part by the Samsung Foundation. Supported in part by the NSF.\n\nPublished - 1_2E9781611973105_2E58.pdf

", "abstract": "We study a generalization of the famous k-center problem where each object is an affine subspace of dimension \u0394, and give either the first or significantly improved algorithms and hardness results for many combinations of parameters. This generalization from points (\u0394 = 0) is motivated by the analysis of incomplete data, a pervasive challenge in statistics: incomplete data objects in \u211dd can be modeled as affine subspaces. We give three algorithmic results for different values of k, under the assumption that all subspaces are axis-parallel, the main case of interest because of the correspondence to missing entries in data tables.\n\n 1) k = 1: Two polynomial time approximation schemes which runs in poly (\u0394, 1/\u220a)nd.\n\n 2) k = 2: O(\u03941/4)-approximation algorithm which runs in poly(n, d, \u0394)\n\n 3) General k: Polynomial time approximation scheme which runs in \n\nWe also prove nearly matching hardness results; in both the general (not necessarily axis-parallel) case (for k \u2265 2) and in the axis-parallel case (for k \u2265 3), the running time of an approximation algorithm with any approximation ratio cannot be polynomial in even one of k and \u0394, unless P = NP. Furthermore, assuming that the 3-SAT problem cannot be solved sub-exponentially, the dependence on both k and \u0394 must be exponential in the general case (in the axis-parallel case, only the dependence on k drops to . The simplicity of the first and the third algorithm suggests that they might be actually used in statistical applications. The second algorithm, which demonstrates a theoretical gap between the axis-parallel and general case for k = 2, displays a strong connection between geometric clustering and classical coloring problems on graphs and hypergraphs, via a new Helly-type theorem.", "date": "2013-01", "date_type": "published", "publisher": "SIAM", "place_of_pub": "Philadelphia, PA", "pagerange": "810-827", "id_number": "CaltechAUTHORS:20161121-172931655", "isbn": "978-1-61197-251-1", "book_title": "Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161121-172931655", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Samsung Foundation" }, { "agency": "NSF" } ] }, "doi": "10.1137/1.9781611973105.58", "primary_object": { "basename": "1_2E9781611973105_2E58.pdf", "url": "https://authors.library.caltech.edu/records/33twp-b8r58/files/1_2E9781611973105_2E58.pdf" }, "resource_type": "book_section", "pub_year": "2013", "author_list": "Lee, Euiwoong and Schulman, Leonard J." }, { "id": "https://authors.library.caltech.edu/records/8b2fj-66088", "eprint_id": 31632, "eprint_status": "archive", "datestamp": "2023-08-19 09:26:09", "lastmod": "2023-10-17 18:44:03", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Feldman-D", "name": { "family": "Feldman", "given": "Dan" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "Data reduction for weighted and outlier-resistant clustering", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2012 SIAM. Work supported in part by the NSF.", "abstract": "Statistical data frequently includes outliers; these can distort the results of estimation procedures and optimization problems. For this reason, loss functions which deemphasize the effect of outliers are widely used by statisticians. However, there are relatively few algorithmic results about clustering with outliers.\nFor instance, the k-median with outliers problem uses a loss function fc_1,...,c_k(x) which is equal to the minimum of a penalty h, and the least distance between the data point x and a center c_i. The loss-minimizing choice of {c_1,..., c_k} is an outlier-resistant clustering of the data. This problem is also a natural special case of the k-median with penalties problem considered by [Charikar, Khuller, Mount and Narasimhan SODA'01].\nThe essential challenge that arises in these optimization problems is data reduction for the weighted k-median problem. We solve this problem, which was previously solved only in one dimension ([Har-Peled FSTTCS'06], [Feldman, Fiat and Sharir FOCS'06]). As a corollary, we also achieve improved data reduction for the k-line-median problem.", "date": "2012-01", "date_type": "published", "publisher": "Society for Industrial and Applied Mathematics", "place_of_pub": "New York, NY", "pagerange": "1343-1354", "id_number": "CaltechAUTHORS:20120524-112316051", "isbn": "9781611972108", "book_title": "Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120524-112316051", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF" } ] }, "resource_type": "book_section", "pub_year": "2012", "author_list": "Feldman, Dan and Schulman, Leonard J." }, { "id": "https://authors.library.caltech.edu/records/mmhdh-yav65", "eprint_id": 31370, "eprint_status": "archive", "datestamp": "2023-08-19 05:08:55", "lastmod": "2023-10-17 16:07:21", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bartal-Y", "name": { "family": "Bartal", "given": "Yair" } }, { "id": "Recht-B", "name": { "family": "Recht", "given": "Ben" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "Dimensionality reduction: beyond the Johnson-Lindenstrauss bound", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2011 SIAM. A previous version of this paper was posted under the title:\n\"A Nash-type Dimensionality Reduction for Discrete Subsets of\nL2\". The work of the first and second authors was performed\nin part while at the Center for the Mathematics of Information,\nCaltech. School of Engineering and Computer Science, Hebrew University, Israel. Supported in part by a grant from the Israeli Science Foundation (195/02) and in part by a\ngrant from the National Science Foundation (NSF CCF-065253). \nSupported in part by NSA H98230-06-1-0074, NSF CCF-0515342 and NSF CCF-0829909.", "abstract": "Dimension reduction of metric data has become a useful technique with numerous applications. The celebrated Johnson-Lindenstrauss lemma states that any n-point subset of Euclidean space can be embedded in O(\u03b5^(\u22122)log n)-dimension with (1 + \u03b5)-distortion. This bound is known to be nearly tight.\nIn many applications the demand that all distances should be nearly preserved is too strong. In this paper we show that indeed under natural relaxations of the goal of the embedding, an improved dimension reduction is possible where the target dimension is independent of n. Our main result can be viewed as a local dimension reduction. There are a variety of empirical situations in which small distances are meaningful and reliable, but larger ones are not. Such situations arise in source coding, image processing, computational biology, and other applications, and are the motivation for widely-used heuristics such as Isomap and Locally Linear Embedding.\nPursuing a line of work begun by Whitney, Nash showed that every C^1 manifold of dimension d can be embedded in R^(2d+2) in such a manner that the local structure at each point is preserved isometrically. Our work is an analog of Nash's for discrete subsets of Euclidean space. For perfect preservation of infinitesimal neighborhoods we substitute near-isometric embedding of neighborhoods of bounded cardinality. We show that any finite subset of Euclidean space can be embedded in O(\u03b5^(\u22122)log k)-dimension while preserving with (1 + \u03b5)-distortion the distances within a \"core neighborhood\" of each point. (The core neighborhood is a metric ball around the point, whose radius is a substantial fraction of the radius of the ball of cardinality k, the k-neighborhood.) When the metric space satisfies a weak growth rate property, the guarantee applies to the entire k-neighborhood (with some dependency of the embedding dimension on the growth rate). We also show how to obtain a global embedding that also keeps distant points well-separated (at the cost of dependency on the doubling dimension of the space).\nAs an application of our methods we obtain an (Assouad-style) dimension reduction for finite subsets of Euclidean space where the metric is raised to some fractional power (the resulting metrics are known as snowflakes). We show that any such metric X can be embedded in dimension \u00d5(\u03b5^(\u22123) dim(X)) with 1 + \u03b5 distortion, where dim(X) is the doubling dimension, a measure of the intrinsic dimension of the set. This result improves recent work by Gottlieb and Krauthgamer [20] to a nearly tight bound.\nThe new dimension reduction results are useful for applications such as clustering and distance labeling.", "date": "2011-01", "date_type": "published", "publisher": "Association for Computing Machinery", "place_of_pub": "New York", "pagerange": "868-887", "id_number": "CaltechAUTHORS:20120509-070406524", "isbn": "978-0-898719-93-2", "book_title": "Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120509-070406524", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Israel Science Foundation", "grant_number": "195/02" }, { "agency": "NSF", "grant_number": "CCF-065253" }, { "agency": "NSA", "grant_number": "H98230-06-1-0074" }, { "agency": "NSF", "grant_number": "CCF-0515342" }, { "agency": "NSF", "grant_number": "CCF-0829909" } ] }, "resource_type": "book_section", "pub_year": "2011", "author_list": "Bartal, Yair; Recht, Ben; et el." }, { "id": "https://authors.library.caltech.edu/records/9n833-z8151", "eprint_id": 72221, "eprint_status": "archive", "datestamp": "2023-08-19 01:19:26", "lastmod": "2023-10-23 20:28:27", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Langberg-M", "name": { "family": "Langberg", "given": "Michael" }, "orcid": "0000-0002-7470-0718" }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "Universal \u03b5-approximators for integrals", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2010 SIAM. \n\nWork supported in part by The Open University of Israel's Rsearch Fund (grant no. 46109) and Cisco Collaborative Research Initiative (CCRI). \n\nWork supported in part by the NSF.\n\nPublished - 1_2E9781611973075_2E50.pdf

", "abstract": "Let X be a space and F a family of 0, 1-valued functions on X. Vapnik and Chervonenkis showed that if F is \"simple\" (finite VC dimension), then for every probability measure \u03bc on X and \u03b5 > 0 there is a finite set S such that for all f \u220a F, \u03c3x\u220aS f(x)/|S| = [\u222b f (x)d\u03bc(x)] \u00b1 \u03b5.\n\nThink of S as a \"universal \u03b5-approximator\" for integration in F. S can actually be obtained w.h.p. just by sampling a few points from \u03bc. This is a mainstay of computational learning theory. It was later extended by other authors to families of bounded (e.g., [0, 1]-valued) real functions.\n\nIn this work we establish similar \"universal \u03b5-approximators\" for families of unbounded nonnegative real functions \u2014 in particular, for the families over which one optimizes when performing data classification. (In this case the \u03b5-approximation should be multiplicative.)\n\nSpecifically, let F be the family of \"k-median functions\" (or k-means, etc.) on \u211dd with an arbitrary norm \u03f1. That is, any set u1, \u2026, uk \u220a \u211dd determines an f by f(x) = (mini \u03f1(x \u2013 ui))\u03b1. (Here \u03b1 \u2265 0.) Then for every measure \u03bc on \u211dd there exists a set S of cardinality poly(k, d, 1/\u03b5) and a measure \u03bd supported on S such that for every f \u220a F, \u03c3x\u220aS f(x)v(x) \u220a (1 \u00b1 \u03b5) \u00b7 (\u222b f(x)d\u03bc(x))", "date": "2010-01", "date_type": "published", "publisher": "SIAM", "place_of_pub": "Philadelphia, PA", "id_number": "CaltechAUTHORS:20161121-163001649", "isbn": "978-0-89871-701-3", "book_title": "Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161121-163001649", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Open University of Israel", "grant_number": "46109" }, { "agency": "Cisco Collaborative Research Initiative (CCRI)" }, { "agency": "NSF" } ] }, "collection": "CaltechAUTHORS", "contributors": { "items": [ { "id": "Charikar-M", "name": { "family": "Charikar", "given": "Moses" } } ] }, "doi": "10.1137/1.9781611973075.50", "primary_object": { "basename": "1_2E9781611973075_2E50.pdf", "url": "https://authors.library.caltech.edu/records/9n833-z8151/files/1_2E9781611973075_2E50.pdf" }, "resource_type": "book_section", "pub_year": "2010", "author_list": "Langberg, Michael and Schulman, Leonard J." }, { "id": "https://authors.library.caltech.edu/records/m2xhy-7zg24", "eprint_id": 71489, "eprint_status": "archive", "datestamp": "2023-08-19 23:23:21", "lastmod": "2023-10-23 15:49:41", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gao-Xiaojie", "name": { "family": "Gao", "given": "Xiaojie" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "On a capacitated multivehicle routing problem", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Algorithms, Theory, Capacitated Multivehicle Routing Problem, Transportation Problem, Resource Allocation, Linear Programming", "note": "\u00a9 2008 ACM. \n\nSupported in part by NSF Award CCF-0515342.", "abstract": "The Vehicle Routing Problem (VRP) is a discrete optimization problem with high industrial relevance and high computational complexity. The problem has been extensively studied since it was introduced by Dantzig and Ramser. In this paper, we present a version of the VRP motivated by mobile sensor networks which we call the Capacitated Multivehicle Routing Problem (CMVRP). Our objective is to determine the minimum amount of energy required to serve all jobs, which takes into account both the service requirement and the travel overhead. We present a constant factor approximation algorithm for the off-line case and a distributed algorithm for the on-line problem that uses only a constant factor more energy than the off-line solution.", "date": "2008-08", "date_type": "published", "publisher": "ACM", "place_of_pub": "New York, NY", "pagerange": "175-184", "id_number": "CaltechAUTHORS:20161025-173435709", "isbn": "978-1-59593-989-0", "book_title": "PODC '08 Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161025-173435709", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-0515342" } ] }, "contributors": { "items": [ { "id": "Bazzi-R", "name": { "family": "Bazzi", "given": "Rida" } } ] }, "doi": "10.1145/1400751.1400776", "resource_type": "book_section", "pub_year": "2008", "author_list": "Gao, Xiaojie and Schulman, Leonard J." }, { "id": "https://authors.library.caltech.edu/records/yr4jp-anj81", "eprint_id": 72617, "eprint_status": "archive", "datestamp": "2023-08-19 22:37:40", "lastmod": "2023-10-23 22:46:51", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Orecchia-Lorenzo", "name": { "family": "Orecchia", "given": "Lorenzo" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" }, { "id": "Vazirani-Umesh-V", "name": { "family": "Vazirani", "given": "Umesh V." } }, { "id": "Vishnoi-Nisheet-K", "name": { "family": "Vishnoi", "given": "Nisheet K." } } ] }, "title": "On partitioning graphs via single commodity flows", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Algorithms, Theory", "note": "\u00a9 2008 ACM. \n\nSupported by NSF Awards CCF-0635401, CCF-0515304, CCF-0635357 and CCR-0121555. Supported by NSA Award H98230-06-1-0074, NSF Award CCF-0515342. Supported by NSF Award CCF-0635401. Part of this work was done when author was visiting UC Berkeley and is supported by NSF Grant CCF-0635401.", "abstract": "In this paper we obtain improved upper and lower bounds for the best approximation factor for Sparsest Cut achievable in the cut-matching game framework proposed in Khandekar et al. [9]. We show that this simple framework can be used to design combinatorial algorithms that achieve O(log n) approximation factor and whose running time is dominated by a poly-logarithmic number of single-commodity max-flow computations. This matches the performance of the algorithm of Arora and Kale [2]. Moreover, we also show that it is impossible to get an approximation factor of better than \u03a9(\u221alog n) in the cut-matching game framework. These results suggest that the simple and concrete abstraction of the cut-matching game may be powerful enough to capture the essential features of the complexity of Sparsest Cut.", "date": "2008-05", "date_type": "published", "publisher": "ACM", "place_of_pub": "New York, NY", "pagerange": "461-470", "id_number": "CaltechAUTHORS:20161206-174428027", "isbn": "978-1-60558-047-0", "book_title": "STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161206-174428027", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-0635401" }, { "agency": "NSF", "grant_number": "CCF-0515304" }, { "agency": "NSF", "grant_number": "CCF-0635357" }, { "agency": "NSF", "grant_number": "CCR-0121555" }, { "agency": "National Security Agency", "grant_number": "H98230-06-1-0074" }, { "agency": "NSF", "grant_number": "CCF-0515342" } ] }, "contributors": { "items": [ { "id": "Ladner-R", "name": { "family": "Ladner", "given": "Richard" } }, { "id": "Dwork-C", "name": { "family": "Dwork", "given": "Cynthia" } } ] }, "doi": "10.1145/1374376.1374442", "resource_type": "book_section", "pub_year": "2008", "author_list": "Orecchia, Lorenzo; Schulman, Leonard J.; et el." }, { "id": "https://authors.library.caltech.edu/records/91kwf-y5f84", "eprint_id": 72748, "eprint_status": "archive", "datestamp": "2023-08-19 21:57:10", "lastmod": "2023-10-23 22:54:31", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rabani-Y", "name": { "family": "Rabani", "given": "Yuval" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" }, { "id": "Swamy-C", "name": { "family": "Swamy", "given": "Chaitanya" } } ] }, "title": "Approximation algorithms for labeling hierarchical taxonomies", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2008 SIAM. \n\nSupported in part by ISF 52/03, BSF 2002282, and the Fund for the Promotion of Research at the Technion. Supported in part by NSF CCF-0515342, NSA H98230-06-1-0074, and NSF ITR CCR-0326554. Research supported partially by NSERC grant 32760-06.\n\nPublished - p671-rabini.pdf

", "abstract": "We consider the following taxonomy labeling problem. Each node of an n-node tree has to be labeled with the values of k attributes. A partial labeling is given as part of the input. The goal is to complete this labeling, minimizing the maximum variation in labeling along an edge. A special case of this problem (which we call the label extension problem), where every node is either completely labeled or not labeled at all, has been considered previously. \n\nWe present an O(log^2 k)-approximation algorithm based on a natural linear programming relaxation. Our results reduce the taxonomy labeling problem to another problem we introduce, called the multicut packing problem (on trees): given k multicommodity flow instances, find a multicut for each instance so as to minimize the maximum number of multicuts that use any single edge. Our algorithm yields an O(log^2 k)-approximation algorithm for this more general problem. We show that the integrality gap of our relaxation is \u03a9(log k), even when applied to the taxonomy labeling problem with 0-1 labels. \n\nFor the label extension problem, we considerably improve the previous O(log n) approximation guarantee and give the first constant-factor approximation algorithm for this problem. Our work relies on relating the label extension problem to questions on Lipschitz extensions of functions into Banach spaces. In particular, our approximation algorithm builds upon Matou\u0161ek's tree metrics extension theorem. Our algorithm also works for other metrics on the label-set, such as edit distance with unit-cost operations, and more generally any shortest path metric induced by an unweighted graph.", "date": "2008-01", "date_type": "published", "publisher": "SIAM", "id_number": "CaltechAUTHORS:20161212-164128630", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161212-164128630", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Israel Science Foundation", "grant_number": "52/03" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2002282" }, { "agency": "Fund for the Promotion of Research at the Technion" }, { "agency": "NSF", "grant_number": "CCF-0515342" }, { "agency": "National Security Agency", "grant_number": "H98230-06-1-0074" }, { "agency": "NSF", "grant_number": "CCR-0326554" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "32760-06" } ] }, "primary_object": { "basename": "p671-rabini.pdf", "url": "https://authors.library.caltech.edu/records/91kwf-y5f84/files/p671-rabini.pdf" }, "resource_type": "book_section", "pub_year": "2008", "author_list": "Rabani, Yuval; Schulman, Leonard J.; et el." }, { "id": "https://authors.library.caltech.edu/records/h917f-mb527", "eprint_id": 77376, "eprint_status": "archive", "datestamp": "2023-08-19 18:42:23", "lastmod": "2023-10-25 22:58:49", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ostrovsky-R", "name": { "family": "Ostrovsky", "given": "Rafail" } }, { "id": "Rabani-Y", "name": { "family": "Rabani", "given": "Yuval" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" }, { "id": "Swamy-C", "name": { "family": "Swamy", "given": "Chaitanya" } } ] }, "title": "The Effectiveness of Lloyd-Type Methods for the k-Means Problem", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2006 IEEE. \n\nSupported in part by IBM Faculty Award, Xerox Innovation Group Award, a gift from Teradata, Intel equipment grant, and NSF Cybertrust grant no. 0430254. Supported in part by ISF 52/03, BSF 2002282, and the Fund for the Promotion of Research at the Technion. Supported in part by NSF CCF-0515342, NSA H98230-06-1-0074, and NSF ITR CCR-0326554.\n\nPublished - 04031353.pdf

", "abstract": "We investigate variants of Lloyd's heuristic for clustering high dimensional data in an attempt to explain its popularity (a half century after its introduction) among practitioners, and in order to suggest improvements in its application. We propose and justify a clusterability criterion for data sets. We present variants of Lloyd's heuristic that quickly lead to provably near-optimal clustering solutions when applied to well-clusterable instances. This is the first performance guarantee for a variant of Lloyd's heuristic. The provision of a guarantee on output quality does not come at the expense of speed: some of our algorithms are candidates for being faster in practice than currently used variants of Lloyd's method. In addition, our other algorithms are faster on well-clusterable instances than recently proposed approximation algorithms, while maintaining similar guarantees on clustering quality. Our main algorithmic contribution is a novel probabilistic seeding process for the starting configuration of a Lloyd-type iteration.", "date": "2006-10", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "165-176", "id_number": "CaltechAUTHORS:20170511-131811663", "isbn": "0-7695-2720-5", "book_title": "47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170511-131811663", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "IBM" }, { "agency": "Xerox" }, { "agency": "Teradata" }, { "agency": "Intel" }, { "agency": "NSF", "grant_number": "CNS-0430254" }, { "agency": "Israel Science Foundation", "grant_number": "52/03" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2002282" }, { "agency": "Technion" }, { "agency": "NSF", "grant_number": "CCF-0515342" }, { "agency": "National Security Agency", "grant_number": "H98230-06-1-0074" }, { "agency": "NSF", "grant_number": "CCR-0326554" } ] }, "doi": "10.1109/FOCS.2006.75", "primary_object": { "basename": "04031353.pdf", "url": "https://authors.library.caltech.edu/records/h917f-mb527/files/04031353.pdf" }, "resource_type": "book_section", "pub_year": "2006", "author_list": "Ostrovsky, Rafail; Rabani, Yuval; et el." }, { "id": "https://authors.library.caltech.edu/records/4k7mq-2bj70", "eprint_id": 71486, "eprint_status": "archive", "datestamp": "2023-08-19 17:10:00", "lastmod": "2023-10-23 15:49:24", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gao-Jie", "name": { "family": "Gao", "given": "Jie" } }, { "id": "Langberg-M", "name": { "family": "Langberg", "given": "Michael" }, "orcid": "0000-0002-7470-0718" }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "Analysis of incomplete data and an intrinsic-dimension Helly theorem", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2006 SIAM. \n\nM. Langberg is supported in part by NSF grant CCF-0346991. L. Schulman is supported in part by an NSF ITR and the Okawa Foundation.\n\nPublished - p464-gao.pdf

", "abstract": "The analysis of incomplete data is a long-standing challenge in practical statistics. When, as is typical, data objects are represented by points in \u211d^d, incomplete data objects correspond to affine subspaces (lines or \u0394-flats). With this motivation we study the problem of finding the minimum intersection radius r(L) of a set of lines or \u0394-flats L: the least r such that there is a ball of radius r intersecting every flat in L. Known algorithms for finding the minimum enclosing ball for a point set (or clustering by several balls) do not easily extend to higher-dimensional flats, primarily because \"distances\" between flats do not satisfy the triangle inequality. In this paper we show how to restore geometry (i.e., a substitute for the triangle inequality) to the problem, through a new analog of Helly's theorem. This \"intrinsic-dimension\" Helly theorem states: for any family L of \u0394-dimensional convex sets in a Hilbert space, there exist \u0394 + 2 sets L' \u2286 L such that r(L) \u2264 2r(L'). Based upon this we present an algorithm that computes a (1 + \u03b5)-core set L' \u2286 L,|L'| = O(\u0394^4/\u03b5^2), such that the ball centered at a point c with radius (1 + \u03b5)r(L') intersects every element of L. The running time of the algorithm is O(n\u0394+1dpoly(1/\u03b5)). For the case of lines or line segments (\u0394 = 1), the (expected) running time of the algorithm can be improved to O(nd poly(1/\u03b5)). We note that the size of the core set depends only on the dimension of the input objects and is independent of the input size n and the dimension d of the ambient space.", "date": "2006-01", "date_type": "published", "publisher": "SIAM", "place_of_pub": "Philadelphia, PA", "pagerange": "464-473", "id_number": "CaltechAUTHORS:20161025-171347433", "isbn": "0-89871-605-5", "book_title": "SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161025-171347433", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-0346991" }, { "agency": "Okawa Foundation" } ] }, "primary_object": { "basename": "p464-gao.pdf", "url": "https://authors.library.caltech.edu/records/4k7mq-2bj70/files/p464-gao.pdf" }, "resource_type": "book_section", "pub_year": "2006", "author_list": "Gao, Jie; Langberg, Michael; et el." }, { "id": "https://authors.library.caltech.edu/records/wk81n-rqg78", "eprint_id": 24948, "eprint_status": "archive", "datestamp": "2023-08-19 16:43:45", "lastmod": "2024-01-13 05:20:30", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ko-C-K", "name": { "family": "Ko", "given": "Chih-Kai" } }, { "id": "Gao-X", "name": { "family": "Gao", "given": "Xiaojie" } }, { "id": "Prajna-S", "name": { "family": "Prajna", "given": "Stephen" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "On Scalar LQG Control with Communication Cost", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2005 IEEE. Date of Current Version: 30 January 2006. This research is supported in part by a NSF Graduate Research\nFellowship.", "abstract": "We study the LQG control of scalar systems under communication constraints by naturally extending the LQG cost to include a quadratic penalty for communication. We show that the resulting optimization problem is quasiconvex in the communications parameter so that it can be solved in a computationally efficient manner.", "date": "2005-12", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, N.J.", "pagerange": "2805-2810", "id_number": "CaltechAUTHORS:20110818-154937885", "isbn": "0-7803-9567-0", "book_title": "2005 44th IEEE Conference on Decision and Control & European Control Conference", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110818-154937885", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF Graduate Research Fellowship" } ] }, "doi": "10.1109/CDC.2005.1582588", "resource_type": "book_section", "pub_year": "2005", "author_list": "Ko, Chih-Kai; Gao, Xiaojie; et el." }, { "id": "https://authors.library.caltech.edu/records/84d3g-fe475", "eprint_id": 25083, "eprint_status": "archive", "datestamp": "2023-08-19 16:26:48", "lastmod": "2023-10-24 15:36:18", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ostrovsky-R", "name": { "family": "Ostrovsky", "given": "Rafail" } }, { "id": "Rabani-Y", "name": { "family": "Rabani", "given": "Yuval" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "Error-correcting codes for automatic control", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2005 IEEE. \n\nIssue Date: 23-25 Oct. 2005. Date of Current Version: 14 November 2005.\n\nPublished - OSTfocs05.pdf

", "abstract": "In many control-theory applications one can classify all possible states of the device by an infinite state graph with polynomially-growing expansion. In order for a controller to control or estimate the state of such a device, it must receive reliable communications from its sensors; if there is channel noise, the encoding task is subject to a stringent real-time constraint. We show a constructive on-line error correcting code that works for this class of applications. Our code is computationally efficient and enables on-line estimation and control in the presence of channel noise. It establishes a constructive (and optimal-within-constants) analog, for control applications, of the Shannon coding theorem.", "date": "2005-10", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Los Alamitos, CA", "pagerange": "309-316", "id_number": "CaltechAUTHORS:20110824-152034750", "isbn": "0-7695-2468-0", "book_title": "46th Annual IEEE Symposium on Foundations of Computer Science", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110824-152034750", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1109/SFCS.2005.33", "primary_object": { "basename": "OSTfocs05.pdf", "url": "https://authors.library.caltech.edu/records/84d3g-fe475/files/OSTfocs05.pdf" }, "resource_type": "book_section", "pub_year": "2005", "author_list": "Ostrovsky, Rafail; Rabani, Yuval; et el." }, { "id": "https://authors.library.caltech.edu/records/hjtfv-bjs31", "eprint_id": 24964, "eprint_status": "archive", "datestamp": "2023-08-19 16:26:43", "lastmod": "2024-01-13 05:20:45", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Moore-C", "name": { "family": "Moore", "given": "Cristopher" } }, { "id": "Russell-A", "name": { "family": "Russell", "given": "Alexander" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "The symmetric group defies strong Fourier sampling", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2005 IEEE.\nIssue Date: 23-25 Oct. 2005.\nDate of Current Version: 14 November 2005.\nThis work was supported by NSF through grants CCR-\n0093065, PHY-0200909, EIA-0218443, EIA-0218563,\nCCR-0220070, CCR-0220264, CCR-0049092, the Institute\nfor Quantum Information, and ARDA under ARO contract\nW911NF-04-R-0009. We are grateful to Denis Th\u00b4erien,\nMcGill University, and Bellairs Research Institute for organizing\na workshop at which this work began; to Dorit\nAharonov, Daniel Rockmore, and Umesh Vazirani for helpful\nconversations; to Chris Lomont for pointing out several\ntypos; and to Tracy Conrad and Sally Milius for their\nsupport and tolerance. C.M. also thanks Rosemary for her\ntimely arrival, and for providing a larger perspective.", "abstract": "We resolve the question of whether Fourier sampling\ncan efficiently solve the hidden subgroup problem in general\ngroups. Specifically, we show that the hidden subgroup\nproblem in the symmetric group cannot be efficiently solved\nby strong Fourier sampling. Indeed we prove the stronger\nstatement that no measurement of a single coset state can\nreveal more than an exponentially small amount of information about the identity of the hidden subgroup, in the special case relevant to the Graph Isomorphism problem.", "date": "2005-10", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Los Alamitos, CA", "pagerange": "479-488", "id_number": "CaltechAUTHORS:20110822-081948476", "isbn": "0-7695-2468-0", "book_title": "46th Annual IEEE Symposium on Foundations of Computer Science", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110822-081948476", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCR-0093065" }, { "agency": "NSF", "grant_number": "PHY-0200909" }, { "agency": "NSF", "grant_number": "EIA-0218443" }, { "agency": "NSF", "grant_number": "EIA-0218563" }, { "agency": "NSF", "grant_number": "CCR-0220070" }, { "agency": "NSF", "grant_number": "CCR-0220264" }, { "agency": "NSF", "grant_number": "CCR-0049092" }, { "agency": "Institute for Quantum Information" }, { "agency": "ARDA", "grant_number": "W911NF-04-R-0009" } ] }, "other_numbering_system": { "items": [ { "id": "8803116", "name": "INSPEC Accession Number" } ] }, "doi": "10.1109/SFCS.2005.73", "resource_type": "book_section", "pub_year": "2005", "author_list": "Moore, Cristopher; Russell, Alexander; et el." }, { "id": "https://authors.library.caltech.edu/records/hbz9e-ag880", "eprint_id": 24905, "eprint_status": "archive", "datestamp": "2023-08-19 16:17:09", "lastmod": "2023-10-24 15:02:10", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gao-X", "name": { "family": "Gao", "given": "Xiaojie" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "Real-Time Coding for Multiple Access Channels", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2005 IEEE. \nIssue Date: 4-9 Sept. 2005.\nDate of Current Version: 31 October 2005. The authors would like to thank the anonymous referees for many helpful suggestions.", "abstract": "We consider a multiple access channel shared by two sources. The channel is noiseless but there is interference between the transmissions of the sources. Because of applications to distributed control we are interested in the real-time version of this problem, in which the receiver must act immediately upon received information. Block coding is therefore not possible, and error probability cannot generally be made to tend to 0 in the interior of the multiple access capacity region. We study code design for a simple class of XOR channels. We provide several computationally efficient design methods. Under an assumption on the form of the correlation among the sources, one of these algorithms provides codes whose success probability is within 2/3 of optimal. In the absence of assumptions on the correlation, optimal code design is NP-hard.", "date": "2005-09", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "67-71", "id_number": "CaltechAUTHORS:20110817-093537514", "isbn": "0-7803-9150-0", "book_title": "2005 IEEE International Symposium on Information Theory", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110817-093537514", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "other_numbering_system": { "items": [ { "id": "9035025", "name": "INSPEC Accession Number" } ] }, "doi": "10.1109/ISIT.2005.1523294", "resource_type": "book_section", "pub_year": "2005", "author_list": "Gao, Xiaojie and Schulman, Leonard J." }, { "id": "https://authors.library.caltech.edu/records/4ngkk-44b97", "eprint_id": 71488, "eprint_status": "archive", "datestamp": "2023-08-19 16:02:06", "lastmod": "2023-10-23 15:49:34", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gao-Xiaojie", "name": { "family": "Gao", "given": "Xiaojie" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "Feedback control for router congestion resolution", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Algorithms, Design, game theory, feedback control, congestion control, Nash Equilibrium, max-min-fairness", "note": "\u00a9 2005 ACM. \n\nSupported in part by the National Science Foundation under grant no. 0049092 and by the Okawa Foundation.", "abstract": "Queueing is a crucial component in effective router congestion control. If packets are dropped indiscriminately by the queueing system, in some cases, the effect can be to encourage senders to actually increase their transmission rates, worsening the congestion and destabilizing the system. \n\nWe approach this congestion problem from the point of view of the elementary concepts of game theory and control theory. We provide a queueing mechanism with feedback-control. Our analysis shows that the protocol achieves high throughput as well as fairness in allocating capacity among sources, while maintaining bounded queue lengths and responding dynamically to changes in network flow conditions. Perhaps most importantly, the new protocol is shown in network simulations to have superior ability (compared with previous solutions) to protect responsive flows (specifically TCP) against router flooding by multiple high-volume unresponsive (e.g., UDP) flows.", "date": "2005-07", "date_type": "published", "publisher": "ACM", "place_of_pub": "New York, NY", "pagerange": "218-226", "id_number": "CaltechAUTHORS:20161025-172835471", "isbn": "1-58113-994-2", "book_title": "PODC '05 Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161025-172835471", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-0049092" }, { "agency": "Okawa Foundation" } ] }, "contributors": { "items": [ { "id": "Aguilera-M", "name": { "family": "Aguilera", "given": "Marcos" } } ] }, "doi": "10.1145/1073814.1073855", "resource_type": "book_section", "pub_year": "2005", "author_list": "Gao, Xiaojie and Schulman, Leonard J." }, { "id": "https://authors.library.caltech.edu/records/29xf4-4th78", "eprint_id": 7339, "eprint_status": "archive", "datestamp": "2023-08-22 03:02:52", "lastmod": "2023-10-16 20:50:55", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Effros-M", "name": { "family": "Effros", "given": "Michelle" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "Rapid near-optimal VQ design with a deterministic data net", "ispublished": "unpub", "full_text_status": "public", "keywords": "approximation theory; combined source-channel coding; vector quantization; source code design; source coding theory; network information theory", "note": "\u00a9 Copyright 2004 IEEE. Reprinted with permission. \n\nM. Effros is partially supported by NSF CCR-0220039 and Caltech's Lee Center for Advanced Networking. \n\nL.J. Schulman is partially supported by NSF CCR-0049092, the Charles Lee Powell Foundation, and a visiting membership at MSRI.", "abstract": "We present a new algorithm for fixed-rate vector quantizer (VQ) design with deterministic data net. The algorithm also performs efficient VQ design for simply characterized continuous distributions. The algorithm also serves as an approximation algorithm for the d-dimensional fixed-rate operational distortion-rate function, extends to a variety of network VQ problems. The algorithm generalizes to give /spl epsiv/-approximation algorithms for many network VQ design problems. A few examples are multiresolution VQ (MRVQ), multiple description VQ (MDVQ), side information VQ (SIVQ), Broadcast VQ (BCVQ), joint source-channel VQ (JSCVQ) and remote source VQ (RSVQ).", "date": "2005-01-10", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Los Alamitos, CA", "pagerange": "299", "id_number": "CaltechAUTHORS:EFFisit04", "isbn": "0-7803-8280-3", "book_title": "IEEE International Symposium on Information Theory (ISIT '04), Chicago, IL, 27 June - 2 July 2004", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:EFFisit04", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1109/ISIT.2004.1365336", "primary_object": { "basename": "EFFisit04.pdf", "url": "https://authors.library.caltech.edu/records/29xf4-4th78/files/EFFisit04.pdf" }, "resource_type": "book_section", "pub_year": "2005", "author_list": "Effros, Michelle and Schulman, Leonard J." }, { "id": "https://authors.library.caltech.edu/records/axmph-qvd87", "eprint_id": 71487, "eprint_status": "archive", "datestamp": "2023-08-19 12:52:53", "lastmod": "2023-10-23 15:49:27", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gao-Xiaojie", "name": { "family": "Gao", "given": "Xiaojie" } }, { "id": "Jain-Kamal", "name": { "family": "Jain", "given": "Kamal" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "Fair and efficient router congestion control", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2004 by the Association for Computing Machinery, Inc. and the Society for industrial and Applied Mathematics. \n\nSupported by National Science Foundation grant no. 0049092 and by the Charles Lee Powell Foundation.\n\nPublished - p1050-gao.pdf

", "abstract": "Congestion is a natural phenomenon in any network queuing system, and is unavoidable if the queuing system is operated near capacity. In this paper we study how to set the rules of a queuing system so that all the users have a self-interest in controlling congestion when it happens. \n\nRouters in the internet respond to local congestion by dropping packets. But if packets are dropped indiscriminately, the effect can be to encourage senders to actually increase their transmission rates, worsening the congestion and destabilizing the system. Alternatively, and only slightly more preferably, the effect can be to arbitrarily let a few insistent senders take over most of the router capacity. \n\nWe approach this problem from first principles: a router packet-dropping protocol is a mechanism that sets up a game between the senders, who are in turn competing for link capacity. Our task is to design this mechanism so that the game equilibrium is desirable: high total rate is achieved and is shared widely among all senders. In addition, equilibrium should be reestablished quickly in response to changes in transmission rates. Our solution is based upon auction theory: in principle, although not always in practice, we drop packets of the highest-rate sender, in case of congestion. We will prove the game-theoretic merits of our method. We'll also describe a variant of the method with some further advantages that will be supported by network simulations.", "date": "2004-01", "date_type": "published", "publisher": "SIAM", "place_of_pub": "Philadelphia, PA", "pagerange": "1050-1059", "id_number": "CaltechAUTHORS:20161025-172050851", "isbn": "0-89871-558-X", "book_title": "SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161025-172050851", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-0049092" }, { "agency": "Charles Lee Powell Foundation" } ] }, "primary_object": { "basename": "p1050-gao.pdf", "url": "https://authors.library.caltech.edu/records/axmph-qvd87/files/p1050-gao.pdf" }, "resource_type": "book_section", "pub_year": "2004", "author_list": "Gao, Xiaojie; Jain, Kamal; et el." }, { "id": "https://authors.library.caltech.edu/records/kcn13-8m180", "eprint_id": 72484, "eprint_status": "archive", "datestamp": "2023-08-19 12:52:58", "lastmod": "2023-10-23 22:39:08", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Moore-C", "name": { "family": "Moore", "given": "Cristopher" } }, { "id": "Rockmore-D", "name": { "family": "Rockmore", "given": "Daniel" } }, { "id": "Russell-A", "name": { "family": "Russell", "given": "Alexander" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "The power of basis selection in fourier sampling: hidden subgroup problems in affine groups", "ispublished": "unpub", "full_text_status": "public", "note": "Copyright \u00a9 2004 by the Association for Computing Machinery, Inc. and the Society for industrial and Applied Mathematics. \n\nWe are grateful to Wim van Dam, Frederic Magniez, Martin R\u00f6tteler, and Miklos Santha for helpful conversations, and to Sally Milius and Tracy Conrad for their support. Support for this work was provided by the California Institute of Technology's Institute for Quantum Information (IQI), the Mathematical Sciences Research Institute (MSRI), the Institute for Advanced Study (IAS), NSF grants ITR-0220070, ITR-0220264, CCR-0093065, EIA-0218443, QuBIC-0218563, the Charles Lee Powell Foundation, and the Bell Fund.\n\nPublished - p1113-moore.pdf

", "abstract": "Many quantum algorithms, including Shor's celebrated factoring and discrete log algorithms, proceed by reduction to a hidden subgroup problem, in which a unknown subgroup H of a group G must be determined from a quantum state \u03c8 over G that is uniformly supported on a left coset of H. These hidden subgroup problems are typically solved by Fourier sampling: the quantum Fourier transform of \u03c8 is computed and measured. When the underlying group is nonabelian, two important variants of the Fourier sampling paradigm have been identified: the weak standard method, where only representation names are measured, and the strong standard method, where full measurement (i.e., the row and column of the representation as well as its name) occurs. It has remained open whether the strong method is indeed stronger, that is, whether there are hidden subgroups that can be reconstructed via the strong method but not by the weak, or any other known, method.In this article, we settle this question in the affirmative. We show that hidden subgroups of semidirect products of the form \u2124q \u00d7 \u2124p, where q | (p - 1) and q = p/polylog(p), can be efficiently determined by the strong standard method. Furthermore, the weak standard method and the \"forgetful\" abelian method are insufficient for these groups so that, in fact, it appears that use of the corresponding nonabelian representation theory is crucial. We extend this to an informationtheoretic solution for the hidden subgroup problem over the groups \u2124q \u00d7 \u2124p where q | (p - 1) and, in particular, the affine groups Ap. Finally, we prove a simple closure property for the class of groups over which the hidden subgroup problem can be solved efficiently.", "date": "2004-01", "date_type": "published", "publisher": "SIAM", "place_of_pub": "Philadelphia, PA", "pagerange": "1113-1122", "id_number": "CaltechAUTHORS:20161130-165912905", "isbn": "0-89871-558-X", "book_title": "SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161130-165912905", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Institute for Quantum Information" }, { "agency": "Mathematical Sciences Research Institute (MSRI)" }, { "agency": "Institute for Advanced Study" }, { "agency": "NSF", "grant_number": "ITR- 022007" }, { "agency": "NSF", "grant_number": "ITR-0220264" }, { "agency": "NSF", "grant_number": "CCR-0093065" }, { "agency": "NSF", "grant_number": "EIA-0218443" }, { "agency": "NSF", "grant_number": "QuBIC-021856" }, { "agency": "Charles Lee Powell Foundation" }, { "agency": "Bell Fund" } ] }, "contributors": { "items": [ { "id": "Munro-I", "name": { "family": "Munro", "given": "Ian" } } ] }, "primary_object": { "basename": "p1113-moore.pdf", "url": "https://authors.library.caltech.edu/records/kcn13-8m180/files/p1113-moore.pdf" }, "resource_type": "book_section", "pub_year": "2004", "author_list": "Moore, Cristopher; Rockmore, Daniel; et el." }, { "id": "https://authors.library.caltech.edu/records/dpvb8-wyd20", "eprint_id": 27595, "eprint_status": "archive", "datestamp": "2023-08-19 09:22:31", "lastmod": "2023-10-24 17:16:18", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Goldreich-O", "name": { "family": "Goldreich", "given": "Oded" } }, { "id": "Karloff-H", "name": { "family": "Karloff", "given": "Howard" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" }, { "id": "Trevisan-L", "name": { "family": "Trevisan", "given": "Luca" } } ] }, "title": "Lower Bounds for Linear Locally Decodable Codes and Private Information Retrieval", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2002 IEEE. \n\nDate of Current Version: 07 August 2002. \n\nWe are grateful to Alex Samorodnitsky for suggesting to us the information-theoretic proof of Lemma 3.3 and allowing us to present it in Section 3.4. Thanks also to Noga Alon for providing us with a proof of Lemma 3.5 and allowing us to reproduce it in our technical report [5].\n\nPublished - GOLaccc02.pdf

", "abstract": "We prove that if a linear error-correcting code C: {0, 1}^n \u2192 {0, 1}^m is such that a bit of the message can be probabilistically reconstructed by looking at two entries of a corrupted codeword, then m = 2^(\u03a9(n)). We also present several extensions of this result. We show a reduction from the complexity, of one-round, information-theoretic private information retrieval systems (with two servers) to locally decodable codes, and conclude that if all the servers' answers are linear combinations of the database content, then t = \u03a9(n/2^a), where t is the length of the user's query and a is the length of the servers' answers. Actually, 2^a can be replaced by O(a^k), where k is the number of bit locations in the answer that are actually inspected in the reconstruction.", "date": "2002-05", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Los Alamitos, CA", "pagerange": "143-151", "id_number": "CaltechAUTHORS:20111102-143056331", "isbn": "0-7695-1468-5", "book_title": "17th IEEE Annual Conference on Computational Complexity", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111102-143056331", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "TAPIR" } ] }, "doi": "10.1109/CCC.2002.1004353", "primary_object": { "basename": "GOLaccc02.pdf", "url": "https://authors.library.caltech.edu/records/dpvb8-wyd20/files/GOLaccc02.pdf" }, "resource_type": "book_section", "pub_year": "2002", "author_list": "Goldreich, Oded; Karloff, Howard; et el." }, { "id": "https://authors.library.caltech.edu/records/c0qkx-v8885", "eprint_id": 71636, "eprint_status": "archive", "datestamp": "2023-08-19 07:56:33", "lastmod": "2023-10-23 15:58:27", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Grigni-M", "name": { "family": "Grigni", "given": "Michaelangelo" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" }, { "id": "Vazirani-Monica-J", "name": { "family": "Vazirani", "given": "Monica" } }, { "id": "Vazirani-Umesh-V", "name": { "family": "Vazirani", "given": "Umesh" } } ] }, "title": "Quantum mechanical algorithms for the nonabelian hidden subgroup problem", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2001 ACM. \n\nSupported in part by NSF grant CCR-9820931. Supported in part by NSF CAREER grant CCR-98761722, the NSF Institute for Quantum Information, and the Charles Lee Powell Foundation. Supported in part by an NSF Mathematical Sciences Postdoctoral Fellowship. Supported in part by NSF grant CCR-9800024 and Darpa grant F30602-00-2-0601.", "abstract": "We provide positive and negative results concerning the \"standard method\" of identifying a hidden subgroup of a nonabelian group using a quantum computer.", "date": "2001-07", "date_type": "published", "publisher": "ACM", "place_of_pub": "New York, NY", "pagerange": "68-74", "id_number": "CaltechAUTHORS:20161031-162455553", "isbn": "1-58113-349-9", "book_title": "STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161031-162455553", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCR-9820931" }, { "agency": "NSF", "grant_number": "CCR-98761722" }, { "agency": "Institute for Quantum Information" }, { "agency": "Charles Lee Powell Foundation" }, { "agency": "NSF Postdoctoral Fellowship" }, { "agency": "NSF", "grant_number": "CCR-9800024" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)", "grant_number": "F30602-00-2-0601" } ] }, "contributors": { "items": [ { "id": "Vitter-J-S", "name": { "family": "Vitter", "given": "Jeffrey S." } }, { "id": "Spirakis-P", "name": { "family": "Spirakis", "given": "Paul" } }, { "id": "Yannakakis-M", "name": { "family": "Yannakakis", "given": "Mihalis" } } ] }, "doi": "10.1145/380752.380769", "resource_type": "book_section", "pub_year": "2001", "author_list": "Grigni, Michaelangelo; Schulman, Leonard J.; et el." }, { "id": "https://authors.library.caltech.edu/records/cpr56-npp98", "eprint_id": 28821, "eprint_status": "archive", "datestamp": "2023-08-19 03:27:54", "lastmod": "2023-10-24 18:10:34", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Cardoze-D-E", "name": { "family": "Cardoze", "given": "David E." } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "Pattern Matching for Spatial Point Sets", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1998 IEEE. Date of Current Version: 06 August 2002. Thanks to Amihood Amir and Piotr Indyk for helpful communications.", "abstract": "Two sets of points in d-dimensional space are given: a data set D consisting of N points, and a pattern set or probe P consisting of k points. We address the problem of determining whether there is a transformation, among a specified group of transformations of the space, carrying P into or near (meaning at a small directed Hausdorff distance of) D. The groups we consider are translations and rigid motions. Runtimes of approximately O(nlogn) and O(n^dlogn) respectively are obtained (letting n=max{N,k} and omitting the effects of several secondary parameters). For translations, a runtime of approximately O(n(ak+1)log^2n) is obtained for the case that a constant fraction \u03b1<1 of the points of the probe is allowed to fail to match.", "date": "1998-11", "date_type": "published", "publisher": "IEEE Computer Society", "place_of_pub": "Los Alamitos, CA", "pagerange": "156-165", "id_number": "CaltechAUTHORS:20120117-151248754", "isbn": "0-8186-9172-7", "book_title": "39th Annual Symposium on Foundations of Computer Science: Proceedings", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120117-151248754", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "other_numbering_system": { "items": [ { "id": "6128780", "name": "INSPEC Accession Number" } ] }, "doi": "10.1109/SFCS.1998.743439", "resource_type": "book_section", "pub_year": "1998", "author_list": "Cardoze, David E. and Schulman, Leonard J." }, { "id": "https://authors.library.caltech.edu/records/e8y67-3px55", "eprint_id": 28455, "eprint_status": "archive", "datestamp": "2023-08-19 03:27:36", "lastmod": "2023-10-24 17:54:44", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ambainis-A", "name": { "family": "Ambainis", "given": "Andris" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" }, { "id": "Ta-Shma-A", "name": { "family": "Ta-Shma", "given": "Amnon" } }, { "id": "Vazirani-Umesh-V", "name": { "family": "Vazirani", "given": "Umesh" } }, { "id": "Wigderson-Avi", "name": { "family": "Wigderson", "given": "Avi" } } ] }, "title": "The quantum communication complexity of sampling", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1998 IEEE. Date of Current Version: 06 August 2002. This research was supported by NSF Grant CCR-9800024, and a JSEP grant. This research was supported by grant number 69/96 of the Israel Science Foundation, founded by the Israel Academy for Sciences and Humanities. The authors would like to thanks Dorit Aharonov, Ike Chuang, Michael Nielsen, Ran Raz and Steven Rudich for very helpful discussions. We thanks Michael Nielsen for showing us how to extend the upper bound of Theorem 1 to the case where M\u03c8 is not normal.", "abstract": "Sampling is an important primitive in probabilistic and quantum algorithms. In the spirit of communication complexity, given a function f: X \u00d7 Y \u2192 {0,1} and a probability distribution D over X \u00d7 Y, we define the sampling complexity of (f,D) as the minimum number of bits Alice and Bob must communicate for Alice to pick x \u2208 X and Bob to pick y \u2208 Y as well as a valve z s.t. the resulting distribution of (x,y,z) is close to the distribution (D,f(D)). In this paper we initiate the study of sampling complexity, in both the classical and quantum model. We give several variants of the definition. We completely characterize some of these tasks, and give upper and lower bounds on others. In particular this allows us to establish an exponential gap between quantum and classical sampling complexity, for the set disjointness function. This is the first exponential gap for any task where the classical probabilistic algorithm is allowed to err.", "date": "1998-11", "date_type": "published", "publisher": "IEEE Computer Society", "place_of_pub": "Los Alamitos, CA", "pagerange": "342-351", "id_number": "CaltechAUTHORS:20111213-142315946", "isbn": "0-8186-9172-7", "book_title": "39th Annual Symposium on Foundations of Computer Science", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111213-142315946", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCR-9800024" }, { "agency": "JSEP" }, { "agency": "Israel Science Foundation", "grant_number": "69/96" } ] }, "other_numbering_system": { "items": [ { "id": "6128800", "name": "INSPEC Accession Number" } ] }, "doi": "10.1109/SFCS.1998.743480", "resource_type": "book_section", "pub_year": "1998", "author_list": "Ambainis, Andris; Schulman, Leonard J.; et el." }, { "id": "https://authors.library.caltech.edu/records/yx1q3-1mz64", "eprint_id": 29216, "eprint_status": "archive", "datestamp": "2023-08-19 00:21:58", "lastmod": "2023-10-24 18:26:24", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rajagopalan-S", "name": { "family": "Rajagopalan", "given": "Sridhar" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "Verifying Identities", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1996 IEEE. Date of Current Version: 06 August 2002. The author thanks the NSF for funding\nDIMACS via NSF grant CCR 91-19999 which supported his stay at DIMACS. We wish to acknowledge helpful conversations with\nManuel Blum, Michaelangelo Grigni, Sampath Kannan\nand Thomas Wilke. We also wish to thank Kousha Etessami\nfor first bringing the question to our attention.", "abstract": "We provide an O\u02dc(n^2) time randomized algorithm to check whether a given operation f:S\u00d7S\u2192S is associative (letting n=|S|). They prove this performance is optimal (up to polylogarithmic factors) even in case the operation is \"cancellative\". No sub-n^3 algorithm was previously known for this task. More generally they give an O(n^c ) time randomized algorithm to check whether a collection of c-ary operations satisfy any given \"read-once\" identity.", "date": "1996-10", "date_type": "published", "publisher": "IEEE Computer Society", "place_of_pub": "Los Alamitos, CA", "pagerange": "612-616", "id_number": "CaltechAUTHORS:20120208-152850561", "isbn": "0-8186-7594-2", "book_title": "Proceedings: 37th Annual Symposium on Foundations of Computer Science", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120208-152850561", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCR 91-19999" } ] }, "collection": "CaltechAUTHORS", "other_numbering_system": { "items": [ { "id": "5444306", "name": "INSPEC Accession Number" } ] }, "doi": "10.1109/SFCS.1996.548520", "resource_type": "book_section", "pub_year": "1996", "author_list": "Rajagopalan, Sridhar and Schulman, Leonard J." }, { "id": "https://authors.library.caltech.edu/records/wq91j-3w168", "eprint_id": 29440, "eprint_status": "archive", "datestamp": "2023-08-20 06:21:41", "lastmod": "2023-10-24 22:12:06", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Naor-M", "name": { "family": "Naor", "given": "Moni" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" }, { "id": "Srinivasan-A", "name": { "family": "Srinivasan", "given": "Aravind" } } ] }, "title": "Splitters and near-optimal derandomization", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1995 IEEE. Date of Current Version: 06 August 2002. We thank Oded Goldreich and Ravi Sundaram for explaining the implication of\nthe construction of (n,k)-universal sets to the non-approximability\nof set cover; and we thank Mike Luby for a discussion. We thank Uri Feige for explaining his results.\n\nSupported by an Alon Fellowship and by a grant from the Israel Science Foundation\nadministered by the Israeli Academy of Sciences", "abstract": "We present a fairly general method for finding deterministic constructions obeying what we call k-restrictions; this yields structures of size not much larger than the probabilistic bound. The structures constructed by our method include (n,k)-universal sets (a collection of binary vectors of length n such that for any subset of size k of the indices, all 2^k configurations appear) and families of perfect hash functions. The near-optimal constructions of these objects imply the very efficient derandomization of algorithms in learning, of fixed-subgraph finding algorithms, and of near optimal \u03a3II\u03a3 threshold formulae. In addition, they derandomize the reduction showing the hardness of approximation of set cover. They also yield deterministic constructions for a local-coloring protocol, and for exhaustive testing of circuits.", "date": "1995-10", "date_type": "published", "publisher": "IEEE Computer Society Press", "place_of_pub": "Los Alamitos, CA", "pagerange": "182-191", "id_number": "CaltechAUTHORS:20120223-112750729", "isbn": "0-8186-7183-1", "book_title": "36th Annual Symposium on Foundations of Computer Science", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120223-112750729", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Alon Fellowship" }, { "agency": "Israel Science Foundation (ISF)" } ] }, "other_numbering_system": { "items": [ { "id": "5125637", "name": "INSPEC Accession Number" } ] }, "doi": "10.1109/SFCS.1995.492475", "resource_type": "book_section", "pub_year": "1995", "author_list": "Naor, Moni; Schulman, Leonard J.; et el." }, { "id": "https://authors.library.caltech.edu/records/57tqs-xjg08", "eprint_id": 29451, "eprint_status": "archive", "datestamp": "2023-08-20 06:15:00", "lastmod": "2023-10-24 22:12:45", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rajagopalan-S", "name": { "family": "Rajagopalan", "given": "Sridhar" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "Coding for Distributed Computation", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1995 IEEE. Date of Current Version: 06 August 2002. Received support from NSF PYI Award CCR 8896202 and\nNSF grant IRI 91-20074 and a DIMACS postdoctoral fellowship.\nSupported in part by an NSF Postdoctoral Fellowship.", "abstract": "We show that any distributed protocol which runs on a noiseless network in time T, can be simulated on an identical noisy network with a slow-down factor proportional to log(d+1), where d is the maximum degree in the network, and with exponentially small probability of error. On every channel of our network we implement communications using tree codes.", "date": "1995-09", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, N.J.", "pagerange": "453-453", "id_number": "CaltechAUTHORS:20120224-093023413", "isbn": "0-7803-2453-6", "book_title": "1995 IEEE International Symposium on Information Theory, Proceedings", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120224-093023413", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF PYI", "grant_number": "CCR 8896202" }, { "agency": "NSF", "grant_number": "IRI-91-20074" }, { "agency": "DIMACS postdoctoral fellowship" }, { "agency": "NSF Postdoctoral Fellowship" } ] }, "other_numbering_system": { "items": [ { "id": "5280200", "name": "INSPEC Accession Number" } ] }, "doi": "10.1109/ISIT.1995.550440", "resource_type": "book_section", "pub_year": "1995", "author_list": "Rajagopalan, Sridhar and Schulman, Leonard J." }, { "id": "https://authors.library.caltech.edu/records/2gn4j-keh80", "eprint_id": 29450, "eprint_status": "archive", "datestamp": "2023-08-20 06:14:54", "lastmod": "2023-10-24 22:12:40", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "Coding for interactive communication", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1995 IEEE. Date of Current Version: 06 August 2002. Supported in part by an NSF Postdoctoral Fellowship.", "abstract": "Let the input to a computation problem be split between two processors connected by a communication link; and let an interactive protocol \u03c0 be known, by which on any input, the processors can solve the problem using no more than T transmissions of bits between them, provided the channel is noiseless. We study the following question: if in fact there is some noise on the channel, what is the effect upon the number of transmissions needed in order to solve the communication problem reliably?.", "date": "1995-09", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, N.J.", "pagerange": "452-452", "id_number": "CaltechAUTHORS:20120224-084221884", "isbn": "0-7803-2453-6", "book_title": "1995 IEEE International Symposium on Information Theory", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120224-084221884", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF Postdoctoral Fellowship" } ] }, "other_numbering_system": { "items": [ { "id": "5280199", "name": "INSPEC Accession Number" } ] }, "doi": "10.1109/ISIT.1995.550439", "resource_type": "book_section", "pub_year": "1995", "author_list": "Schulman, Leonard J." }, { "id": "https://authors.library.caltech.edu/records/612e5-wk075", "eprint_id": 29341, "eprint_status": "archive", "datestamp": "2023-08-20 06:14:32", "lastmod": "2023-10-24 22:07:22", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Evans-W-S", "name": { "family": "Evans", "given": "William S." } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "Information Theory and Noisy Computation", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 1995 IEEE. Date of Current Version: 06 August 2002. Supported by a Canadian International Fellowship and NSF grant CCR 92-01092.\nSupported in part by an NSF Postdoctoral Fellowship.\n\nPublished - EVAisit95.pdf

", "abstract": "We report on two types of results. The first is a study of the rate of decay of information carried by a signal which is being propagated over a noisy channel. The second is a series of lower bounds on the depth, size, and component reliability of noisy logic circuits which are required to compute some function reliably. The arguments used for the circuit results are information-theoretic, and in particular, the signal decay result is essential to the depth lower bound. Our first result can be viewed as a quantified version of the data processing lemma, for the case of Boolean random variables.", "date": "1995-09", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "456", "id_number": "CaltechAUTHORS:20120216-114451513", "isbn": "0-7803-2453-6", "book_title": "Proceedings: 1995 IEEE International Symposium on Information Theory", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120216-114451513", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Canadian International Fellowship" }, { "agency": "NSF", "grant_number": "CCR 92-01092" }, { "agency": "NSF Postdoctoral Fellowship" } ] }, "other_numbering_system": { "items": [ { "id": "5280203", "name": "INSPEC Accession Number" } ] }, "doi": "10.1109/ISIT.1995.550443", "primary_object": { "basename": "EVAisit95.pdf", "url": "https://authors.library.caltech.edu/records/612e5-wk075/files/EVAisit95.pdf" }, "resource_type": "book_section", "pub_year": "1995", "author_list": "Evans, William S. and Schulman, Leonard J." }, { "id": "https://authors.library.caltech.edu/records/5gv8m-ed141", "eprint_id": 29427, "eprint_status": "archive", "datestamp": "2023-08-20 04:44:28", "lastmod": "2023-10-24 22:11:05", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "Coding for distributed computation", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 1994 IEEE.\nDate of Current Version: 06 August 2002.\n\nResearch supported by an NSF Mathematical Sciences\nPostdoctoral Fellowship.\n\nPublished - SCHUwits94.pdf

", "abstract": "The author describes analogous coding theorems for the more general, interactive, communications required in computation. In this case the bits transmitted in the protocol are not known to the processors in advance but are determined dynamically. First he shows that any interactive protocol of length T between two processors connected by a noiseless channel can be simulated, if the channel is noisy (a binary symmetric channel of capacity C), in time proportional to T 1/C, and with error probability exponentially small in T. He then shows that this result can be extended to arbitrary distributed network protocols. He shows that any distributed protocol which runs in time T on a network of degree d having noiseless communication channels, can, if the channels are in fact noisy, be simulated on that network in time proportional to T 1/C log d. The probability of failure of the protocol is exponentially small in T.", "date": "1994-10", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "28-28", "id_number": "CaltechAUTHORS:20120223-084134446", "isbn": "0-7803-2761-6", "book_title": "Proceedings 1994 IEEE-IMS Workshop on Information Theory and Statistics", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120223-084134446", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF Mathematical Sciences Postdoctoral Fellowship" } ] }, "other_numbering_system": { "items": [ { "id": "5111909", "name": "INSPEC Accession Number" } ] }, "doi": "10.1109/WITS.1994.513866", "primary_object": { "basename": "SCHUwits94.pdf", "url": "https://authors.library.caltech.edu/records/5gv8m-ed141/files/SCHUwits94.pdf" }, "resource_type": "book_section", "pub_year": "1994", "author_list": "Schulman, Leonard J." }, { "id": "https://authors.library.caltech.edu/records/wpz9a-b4443", "eprint_id": 29668, "eprint_status": "archive", "datestamp": "2023-08-20 03:15:20", "lastmod": "2024-01-13 05:51:22", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Evans-W", "name": { "family": "Evans", "given": "Williams" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "Signal Propagation, with Application to a Lower Bound on the Depth of Noisy Formulas", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 1993 IEEE. Date of Current Version: 06 August 2002. Research supported in part by NSF grant CCR 92-01092.\nResearch supported by an NSF postdoctoral fellowship. Thanks to N. Pippenger for helpful consultations.\n\nPublished - EVAfocs93.pdf

", "abstract": "We study the decay of an information signal propagating through a series of noisy channels. We obtain exact bounds on such decay, and as a result provide a new lower bound on the depth of formulas with noisy components. This improves upon previous work of N. Pippenger and significantly decreases the gap between his lower bound and the classical upper bound of von Neumann. We also discuss connections between our work and the study of mixing rates of Markov chains.", "date": "1993-11", "date_type": "published", "publisher": "IEEE Computer Society Press", "place_of_pub": "Los Alamitos, CA", "pagerange": "594-603", "id_number": "CaltechAUTHORS:20120309-133211732", "isbn": "0-8186-4370-6", "book_title": "34th Annual Symposium on Foundations of Computer Science Proceedings", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120309-133211732", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCR 92-01092" }, { "agency": "NSF Postdoctoral Fellowship" } ] }, "other_numbering_system": { "items": [ { "id": "4858027", "name": "INSPEC Accession Number" } ] }, "doi": "10.1109/SFCS.1993.366827", "primary_object": { "basename": "EVAfocs93.pdf", "url": "https://authors.library.caltech.edu/records/wpz9a-b4443/files/EVAfocs93.pdf" }, "resource_type": "book_section", "pub_year": "1993", "author_list": "Evans, Williams and Schulman, Leonard J." }, { "id": "https://authors.library.caltech.edu/records/emcss-gjm22", "eprint_id": 29884, "eprint_status": "archive", "datestamp": "2023-08-20 01:44:56", "lastmod": "2023-10-24 22:32:10", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "Communication on noisy channels: a coding theorem for computation", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 1992 IEEE.\nSupport for this research was provided by an ONR graduate\nfellowship, an MIT Applied Mathematics graduate fellowship,\nand grants NSF 8912586 CCR and AFOSR 89-0271.\n\nI thank Mike Sipser, whose encouragement of my\nwork on this project, and supervision of its progress,\nhave been invaluable. Further I thank Peter Elias for\nmuch advice and assistance. For consultations and\ncomments thanks also to Dan Abramovich, Robert Gallager, Wayne Goddard, Mauricio Karchmer, Dan\nKleitman, Mike Klugerman and Andrew Sutherland.\n\nPublished - SCHUfocs92.pdf

", "abstract": "Communication is critical to distributed computing, parallel computing, or any situation in which automata interact-hence its significance as a resource in computation. In view of the likelihood of errors occurring in a lengthy interaction, it is desirable to incorporate this possibility in the model of communication. The author relates the noisy channel and the standard (noise less channel) complexities of a communication problem by establishing a `two-way' or interactive analogue of Shanon's coding theorem: every noiseless channel protocol can be simulated by a private-coin noisy channel protocol whose time bound is proportional to the original (noiseless) time bound and inversely proportional to the capacity of the channel, while the protocol errs with vanishing probability. The method involves simulating the original protocol while implementing a hierarchical system of progress checks which ensure that errors of any magnitude in the simulation are, with high probability, rapidly eliminated.", "date": "1992-10", "date_type": "published", "publisher": "IEEE Computer Society Press", "place_of_pub": "Los Alamitos, CA", "pagerange": "724-733", "id_number": "CaltechAUTHORS:20120328-141319570", "isbn": "0-8186-2900-2", "book_title": "33rd Annual Symposium on Foundations of Computer Science", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120328-141319570", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Office of Naval Research (ONR) Graduate Fellowship" }, { "agency": "MIT Applied Mathematics Graduate Fellowship" }, { "agency": "NSF", "grant_number": "CCR-8912586" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "89-0271" } ] }, "other_numbering_system": { "items": [ { "id": "4498953", "name": "INSPEC Accession Number" } ] }, "doi": "10.1109/SFCS.1992.267778", "primary_object": { "basename": "SCHUfocs92.pdf", "url": "https://authors.library.caltech.edu/records/emcss-gjm22/files/SCHUfocs92.pdf" }, "resource_type": "book_section", "pub_year": "1992", "author_list": "Schulman, Leonard J." }, { "id": "https://authors.library.caltech.edu/records/nd79v-twd14", "eprint_id": 11499, "eprint_status": "archive", "datestamp": "2023-08-22 08:25:27", "lastmod": "2023-10-17 15:06:12", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Awerbuch-B", "name": { "family": "Awerbuch", "given": "Baruch" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" } ] }, "title": "The maintenance of common data in a distributed system", "ispublished": "unpub", "full_text_status": "public", "keywords": "computational complexity; computer networks; database theory; distributed databases; protocols; software maintenance; common data maintenance; common database; communication complexity; deterministic protocol; distributed computation; distributed system; locally generated changes; maintenance protocol; polylogarithmic overhead; time complexity", "note": "\u00a9 Copyright 1991 IEEE. Reprinted with permission. \n\nPublication Date: 1-4 Oct. 1991. \n\nSupported by Air Force Contract TNDGAFOSR-86-0078, ARO contract DAAL03-86-K0171, NSF contract CCR8611442, and a special grant from IBM. Supported by an ONR Graduate Fellowship.\n\nPublished - AWEfocs91.pdf

", "abstract": "A basic task in distributed computation is the maintenance at each processor of the network, of a current and accurate copy of a common database. A primary example is the maintenance, for routing and other purposes, of a record of the current topology of the system. \n\nSuch a database must be updated in the wake of locally generated changes to its contents. Due to previous disconnections of parts of the network, a maintenance protocol may need to update processors holding widely varying versions of the database. \n\nWe provide a deterministic protocol for this problem, which has only polylogarithmic overhead in its time and communication complexities. Previous deterministic solutions required polynomial overhead in at least one of these measures.", "date": "1991-10", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "505-514", "id_number": "CaltechAUTHORS:AWEfocs91", "isbn": "0-8186-2445-0", "book_title": "Foundations of Computer Science, 32nd Annual Symposium. 1-4 Oct. 1991", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:AWEfocs91", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research", "grant_number": "TNDGAFOSR-86-0078" }, { "agency": "Army Research Office", "grant_number": "DAAL03-86-K-0171" }, { "agency": "National Science Foundation", "grant_number": "CCR8611442" }, { "agency": "IBM Corporation" }, { "agency": "Office of Naval Research" } ] }, "doi": "10.1109/SFCS.1991.185413", "primary_object": { "basename": "AWEfocs91.pdf", "url": "https://authors.library.caltech.edu/records/nd79v-twd14/files/AWEfocs91.pdf" }, "resource_type": "book_section", "pub_year": "1991", "author_list": "Awerbuch, Baruch and Schulman, Leonard J." } ]