2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)

7-9 Oct. 2018

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  • [Title page i]

    Publication Year: 2018, Page(s): 1
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  • [Title page iii]

    Publication Year: 2018, Page(s): 3
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  • [Copyright notice]

    Publication Year: 2018, Page(s): 4
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  • Table of contents

    Publication Year: 2018, Page(s):5 - 14
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  • FOCS 2018 Preface

    Publication Year: 2018, Page(s): 15
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  • FOCS 2018 Organizing Committee and Sponsors

    Publication Year: 2018, Page(s): 16
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  • FOCS 2018 Program Committee

    Publication Year: 2018, Page(s): 17
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  • FOCS 2018 External Reviewers

    Publication Year: 2018, Page(s):18 - 21
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  • FOCS 2018 Awards [2 awards]

    Publication Year: 2018, Page(s): 22
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  • Balancing Vectors in Any Norm

    Publication Year: 2018, Page(s):1 - 10
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (224 KB) | HTML iconHTML

    In the vector balancing problem, we are given symmetric convex bodies C and K in Rn, and our goal is to determine the minimum number ß ≥ 0, known as the vector balancing constant from C to K, such that for any sequence of vectors in C there always exists a signed combination of them lying inside ßK. Many fundamental results in discrepancy theory, such as the Beck-Fiala theorem (Discrete Appl. Math... View full abstract»

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  • Metric Sublinear Algorithms via Linear Sampling

    Publication Year: 2018, Page(s):11 - 22
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (270 KB) | HTML iconHTML

    We provide a new technique to design fast approximation algorithms for graph problems where the points of the graph lie in a metric space. Specifically, we present a sampling approach for such metric graphs that, using a sublinear number of edge weight queries, provides a linear sampling, where each edge is (roughly speaking) sampled proportionally to its weight. For several natural problems, such... View full abstract»

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  • Approximating the Permanent of a Random Matrix with Vanishing Mean

    Publication Year: 2018, Page(s):23 - 34
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (296 KB) | HTML iconHTML

    The permanent is #P-hard to compute exactly on average for natural random matrices including matrices over finite fields or Gaussian ensembles. Should we expect that it remains #P-hard to compute on average if we only care about approximation instead of exact computation? In this work we take a first step towards resolving this question: We present a quasi-polynomial time deterministic algorithm f... View full abstract»

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  • Log-Concave Polynomials, Entropy, and a Deterministic Approximation Algorithm for Counting Bases of Matroids

    Publication Year: 2018, Page(s):35 - 46
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (283 KB) | HTML iconHTML

    We give a deterministic polynomial time 2^O(r)-approximation algorithm for the number of bases of a given matroid of rank r and the number of common bases of any two matroids of rank r. To the best of our knowledge, this is the first nontrivial deterministic approximation algorithm that works for arbitrary matroids. Based on a lower bound of Azar, Broder, and Frieze this is almost the best possibl... View full abstract»

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  • A Short List of Equalities Induces Large Sign Rank

    Publication Year: 2018, Page(s):47 - 58
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (261 KB) | HTML iconHTML

    We exhibit a natural function F, that can be computed by just a linear sized decision list of 'Equalities', but whose sign rank is exponentially large. This yields the following two new unconditional complexity class separations. The first is an exponential separation between the depth-two threshold circuit classes Threshold-of Majority and Threshold-of-Threshold, answering an open question posed ... View full abstract»

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  • Simple Optimal Hitting Sets for Small-Success RL

    Publication Year: 2018, Page(s):59 - 64
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (196 KB) | HTML iconHTML

    We give a simple explicit hitting set generator for read-once branching programs of width w and length r with known variable order. When r = w, our generator has seed length O(log2 r + log(1/ε)). When r = polylog w, our generator has optimal seed length O(log w + log(1/ε)). For intermediate values of r, our generator's seed length smoothly interpolates between these two extremes. Our ge... View full abstract»

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  • Hardness Magnification for Natural Problems

    Publication Year: 2018, Page(s):65 - 76
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (264 KB) | HTML iconHTML

    We show that for several natural problems of interest, complexity lower bounds that are barely non-trivial imply super-polynomial or even exponential lower bounds in strong computational models. We term this phenomenon “hardness magnification”. Our examples of hardness magnification include: 1) Let MCSP[s] be the decision problem whose YES instances are truth tables of functions with circuit compl... View full abstract»

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  • Counting t-Cliques: Worst-Case to Average-Case Reductions and Direct Interactive Proof Systems

    Publication Year: 2018, Page(s):77 - 88
    Cited by:  Papers (1)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (283 KB) | HTML iconHTML

    We study two aspects of the complexity of counting the number of t-cliques in a graph: 1) Worst-case to average-case reductions: Our main result reduces counting t-cliques in any n-vertex graph to counting t-cliques in typical n-vertex graphs that are drawn from a simple distribution of min-entropy Ω(n2). For any constant t, the reduction runs in O(n2)-time, and yields a correct answer (w.h.p.) ev... View full abstract»

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  • A Faster Isomorphism Test for Graphs of Small Degree

    Publication Year: 2018, Page(s):89 - 100
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (277 KB) | HTML iconHTML

    In a recent breakthrough, Babai (STOC 2016) gave quasipolynomial graph isomorphism test. In this work, we give an improved isomorphism test for graphs of small degree: our algorithms runs in time n^O((log d)^c), where n is the number of vertices of the input graphs, d is the maximum degree of the input graphs, and c is an absolute constant. The best previous isomorphism test for graphs of maximum ... View full abstract»

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  • Graph Sketching against Adaptive Adversaries Applied to the Minimum Degree Algorithm

    Publication Year: 2018, Page(s):101 - 112
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (232 KB) | HTML iconHTML

    Motivated by the study of matrix elimination orderings in combinatorial scientific computing, we utilize graph sketching and local sampling to give a data structure that provides access to approximate fill degrees of a matrix undergoing elimination in polylogarithmic time per elimination and query. We then study the problem of using this data structure in the minimum degree algorithm, which is a w... View full abstract»

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  • Faster Exact and Approximate Algorithms for k-Cut

    Publication Year: 2018, Page(s):113 - 123
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (272 KB) | HTML iconHTML

    In the k-cut problem, we are given an edge-weighted graph G and an integer k, and have to remove a set of edges with minimum total weight so that G has at least k connected components. The current best algorithms are an O(n(2-o(1))k) randomized algorithm due to Karger and Stein, and an Õ(n2k) deterministic algorithm due to Thorup. Moreover, several 2-approximation algorithms ... View full abstract»

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  • Delegating Computations with (Almost) Minimal Time and Space Overhead

    Publication Year: 2018, Page(s):124 - 135
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (293 KB) | HTML iconHTML

    The problem of verifiable delegation of computation considers a setting in which a client wishes to outsource an expensive computation to a powerful, but untrusted, server. Since the client does not trust the server, we would like the server to certify the correctness of the result. Delegation has emerged as a central problem in cryptography, with a flurry of recent activity in both theory and pra... View full abstract»

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  • Computational Two-Party Correlation: A Dichotomy for Key-Agreement Protocols

    Publication Year: 2018, Page(s):136 - 147
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (250 KB) | HTML iconHTML

    Let π be an efficient two-party protocol that given security parameter k, both parties output single bits Xk and Yk, respectively. We are interested in how (Xk, Yk) "appears" to an efficient adversary that only views the transcript Tk. We make the following contributions: · We develop new tools to argue about this loose notion, and show (modul... View full abstract»

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  • PPP-Completeness with Connections to Cryptography

    Publication Year: 2018, Page(s):148 - 158
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (376 KB) | HTML iconHTML

    Polynomial Pigeonhole Principle (PPP) is an important subclass of TFNP with profound connections to the complexity of the fundamental cryptographic primitives: collision-resistant hash functions and one-way permutations. In contrast to most of the other subclasses of TFNP, no complete problem is known for PPP. Our work identifies the first PPP-complete problem without any circuit or Turing Machine... View full abstract»

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  • Hölder Homeomorphisms and Approximate Nearest Neighbors

    Publication Year: 2018, Page(s):159 - 169
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (284 KB) | HTML iconHTML

    We study bi-Hölder homeomorphisms between the unit spheres of finite-dimensional normed spaces and use them to obtain better data structures for the high-dimensional Approximate Near Neighbor search (ANN) in general normed spaces. Our main structural result is a finite-dimensional quantitative version of the following theorem of Daher (1993) and Kalton (unpublished). Every d-dimensional normed spa... View full abstract»

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  • Near-Optimal Approximate Decremental All Pairs Shortest Paths

    Publication Year: 2018, Page(s):170 - 181
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (264 KB) | HTML iconHTML

    In this paper we consider the decremental approximate all-pairs shortest paths (APSP) problem, where given a graph G the goal is to maintain approximate shortest paths between all pairs of nodes in G under a sequence of online adversarial edge deletions. We present a decremental APSP algorithm for undirected weighted graphs with (2+ε)k-1 stretch, O(mn1/k +o(1)log(nW)) total u... View full abstract»

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