2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)

15-17 Oct. 2017

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  • [Front cover]

    Publication Year: 2017, Page(s): c1
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  • [Title page i]

    Publication Year: 2017, Page(s): i
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  • [Title page iii]

    Publication Year: 2017, Page(s): iii
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  • [Copyright notice]

    Publication Year: 2017, Page(s): iv
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  • Table of contents

    Publication Year: 2017, Page(s):v - xii
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  • Preface

    Publication Year: 2017, Page(s): xiii
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  • Organizing Committee and Sponsors

    Publication Year: 2017, Page(s): xiv
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  • Program Committee

    Publication Year: 2017, Page(s): xv
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  • External reviewers

    Publication Year: 2017, Page(s):xvi - xix
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  • FOCS 2017 Awards

    Publication Year: 2017, Page(s): xx
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  • A Nearly Optimal Lower Bound on the Approximate Degree of AC^0

    Publication Year: 2017, Page(s):1 - 12
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (310 KB) | HTML iconHTML

    The approximate degree of a Boolean function f : {-1, 1}n → {-1, 1} is the least degree of a real polynomial that approximates f pointwise to error at most 1/3. We introduce a generic method for increasing the approximate degree of a given function, while preserving its computability by constant-depth circuits. Specifically, we show how to transform any Boolean function f with ap... View full abstract»

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  • On the Quantitative Hardness of CVP

    Publication Year: 2017, Page(s):13 - 24
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (705 KB) | HTML iconHTML

    For odd integers p ≥ 1 (and p = ∞), we show that the Closest Vector Problem in the ℓp norm (CVPp) over rank n lattices cannot be solved in 2(1-ε)n time for any constant ε > 0 unless the Strong Exponential Time Hypothesis (SETH) fails. We then extend this result to “almost all” values of p ≥ 1, not including... View full abstract»

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  • Distributed PCP Theorems for Hardness of Approximation in P

    Publication Year: 2017, Page(s):25 - 36
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (276 KB) | HTML iconHTML

    We present a new distributed model of probabilistically checkable proofs (PCP). A satisfying assignment x ∈ {0, 1}n to a CNF formula φ is shared between two parties, where Alice knows x1, ... , xn/2, Bob knows xn/2+1, . . . , xn, and both parties know φ. The goal is to have Alice and Bob jointly write a PCP that x satisfies φ,... View full abstract»

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  • Short Presburger Arithmetic Is Hard

    Publication Year: 2017, Page(s):37 - 48
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (319 KB) | HTML iconHTML

    We study the computational complexity of short sentences in Presburger arithmetic (SHORT-PA). Here by “short” we mean sentences with a bounded number of variables, quantifiers, inequalities and Boolean operations; the input consists only of the integer coefficients involved in the linear inequalities. We prove that satisfiability of SHORT-PA sentences with m+2 alternating quantifiers... View full abstract»

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  • On the Local Structure of Stable Clustering Instances

    Publication Year: 2017, Page(s):49 - 60
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (307 KB) | HTML iconHTML

    We study the classic k-median and k-means clustering objectives in the beyond-worst-case scenario. We consider three well-studied notions of structured data that aim at characterizing real-world inputs: Distribution Stability (introduced by Awasthi, Blum, and Sheffet, FOCS 2010); Spectral Separability (introduced by Kumar and Kannan, FOCS 2010); Perturbation Resilience (introduced by Bilu and Lini... View full abstract»

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  • Better Guarantees for k-Means and Euclidean k-Median by Primal-Dual Algorithms

    Publication Year: 2017, Page(s):61 - 72
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (318 KB) | HTML iconHTML

    Clustering is a classic topic in optimization with k-means being one of the most fundamental such problems. In the absence of any restrictions on the input, the best known algorithm for k-means with a provable guarantee is a simple local search heuristic yielding an approximation guarantee of 9 + ε, a ratio that is known to be tight with respect to such methods. We overcome this barrier by ... View full abstract»

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  • Statistical Query Lower Bounds for Robust Estimation of High-Dimensional Gaussians and Gaussian Mixtures

    Publication Year: 2017, Page(s):73 - 84
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (256 KB) | HTML iconHTML

    We describe a general technique that yields the first Statistical Query lower bounds for a range of fundamental high-dimensional learning problems involving Gaussian distributions. Our main results are for the problems of (1) learning Gaussian mixture models (GMMs), and (2) robust (agnostic) learning of a single unknown Gaussian distribution. For each of these problems, we show a super-polynomial ... View full abstract»

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  • On Learning Mixtures of Well-Separated Gaussians

    Publication Year: 2017, Page(s):85 - 96
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (301 KB) | HTML iconHTML

    We consider the problem of efficiently learning mixtures of a large number of spherical Gaussians, when the components of the mixture are well separated. In the most basic form of this problem, we are given samples from a uniform mixture of k standard spherical Gaussians with means μ1, . . . , μk ∈ ℝd, and the goal is to estimate the mea... View full abstract»

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  • On Small-Depth Frege Proofs for Tseitin for Grids

    Publication Year: 2017, Page(s):97 - 108
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (240 KB) | HTML iconHTML

    We prove a lower bound on the size of a small depth Frege refutation of the Tseitin contradiction on the grid. We conclude that polynomial size such refutations must use formulas of almost logarithmic depth. View full abstract»

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  • Random Θ(log n)-CNFs Are Hard for Cutting Planes

    Publication Year: 2017, Page(s):109 - 120
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (313 KB) | HTML iconHTML

    Summary form only given. Strong light-matter coupling has been recently successfully explored in the GHz and THz [1] range with on-chip platforms. New and intriguing quantum optical phenomena have been predicted in the ultrastrong coupling regime [2], when the coupling strength Ω becomes comparable to the unperturbed frequency of the system ω. We recently proposed a new experimental ... View full abstract»

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  • Random Formulas, Monotone Circuits, and Interpolation

    Publication Year: 2017, Page(s):121 - 131
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (289 KB) | HTML iconHTML

    Summary form only given. Strong light-matter coupling has been recently successfully explored in the GHz and THz [1] range with on-chip platforms. New and intriguing quantum optical phenomena have been predicted in the ultrastrong coupling regime [2], when the coupling strength Ω becomes comparable to the unperturbed frequency of the system ω. We recently proposed a new experimental ... View full abstract»

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  • Query-to-Communication Lifting for BPP

    Publication Year: 2017, Page(s):132 - 143
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (329 KB) | HTML iconHTML

    For any n-bit boolean function f, we show that the randomized communication complexity of the composed function f o gn, where g is an index gadget, is characterized by the randomized decision tree complexity of f. In particular, this means that many query complexity separations involving randomized models (e.g., classical vs. quantum) automatically imply analogous separations in communi... View full abstract»

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  • A Rounds vs. Communication Tradeoff for Multi-Party Set Disjointness

    Publication Year: 2017, Page(s):144 - 155
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (298 KB) | HTML iconHTML

    In the set disjointess problem, we have k players, each with a private input Xi ⊆ [n], and the goal is for the players to determine whether or not their sets have a global intersection. The players communicate over a shared blackboard, and we charge them for each bit that they write on the board. We study the trade-off between the number of interaction rounds we allow the players... View full abstract»

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  • A Time Hierarchy Theorem for the LOCAL Model

    Publication Year: 2017, Page(s):156 - 167
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (780 KB) | HTML iconHTML

    The celebrated Time Hierarchy Theorem for Turing machines states, informally, that more problems can be solved given more time. The extent to which a time hierarchy-type theorem holds in the classic distributed LOCAL model has been open for many years. In particular, it is consistent with previous results that all natural problems in the LOCAL model can be classified according to a small constant ... View full abstract»

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  • Distributed Exact Weighted All-Pairs Shortest Paths in Õ(n^{5/4}) Rounds

    Publication Year: 2017, Page(s):168 - 179
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (320 KB) | HTML iconHTML

    We study computing all-pairs shortest paths (APSP) on distributed networks (the CONGEST model). The goal is for every node in the (weighted) network to know the distance from every other node using communication. The problem admits (1+o(1))-approximation Õ(n)-time algorithms [2], [3], which are matched with Ω(n)-time lower bounds [3], [4], [5]1. No ω(n) lower bound... View full abstract»

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