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  • Algorithms for #BIS-Hard Problems on Expander Graphs
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-07-01
    Matthew Jenssen; Peter Keevash; Will Perkins

    SIAM Journal on Computing, Volume 49, Issue 4, Page 681-710, January 2020. We give a fully polynomial-time approximation scheme (FPTAS) and an efficient sampling algorithm for the high-fugacity hard-core model on bounded-degree bipartite expander graphs and the low-temperature ferromagnetic Potts model on bounded-degree expander graphs. The results apply, for example, to random (bipartite) $\Delta$-regular

    更新日期:2020-07-02
  • Graph Sparsification, Spectral Sketches, and Faster Resistance Computation via Short Cycle Decompositions
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-06-09
    Timothy Chu; Yu Gao; Richard Peng; Sushant Sachdeva; Saurabh Sawlani; Junxing Wang

    SIAM Journal on Computing, Ahead of Print. We develop a framework for graph sparsification and sketching, based on a new tool, short cycle decomposition, which is a decomposition of an unweighted graph into an edge-disjoint collection of short cycles, plus a small number of extra edges. A simple observation shows that every graph $G$ on $n$ vertices with $m$ edges can be decomposed in $O(mn)$ time

    更新日期:2020-06-30
  • Shadow Tomography of Quantum States
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-06-30
    Scott Aaronson

    SIAM Journal on Computing, Ahead of Print. We introduce the problem of shadow tomography: given an unknown $D$-dimensional quantum mixed state $\rho$, as well as known two-outcome measurements $E_{1},\ldots,E_{M}$, estimate the probability that $E_{i}$ accepts $\rho$, to within additive error $\varepsilon$, for each of the $M$ measurements. How many copies of $\rho$ are needed to achieve this, with

    更新日期:2020-06-30
  • Finding Cliques in Social Networks: A New Distribution-Free Model
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-04-27
    Jacob Fox; Tim Roughgarden; C. Seshadhri; Fan Wei; Nicole Wein

    SIAM Journal on Computing, Volume 49, Issue 2, Page 448-464, January 2020. We propose a new distribution-free model of social networks. Our definitions are motivated by one of the most universal signatures of social networks, triadic closure---the property that pairs of vertices with common neighbors tend to be adjacent. Our most basic definition is that of a $c$-closed graph, where for every pair

    更新日期:2020-06-30
  • Fair Scheduling via Iterative Quasi-Uniform Sampling
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-06-29
    Sungjin Im; Benjamin Moseley

    SIAM Journal on Computing, Volume 49, Issue 3, Page 658-680, January 2020. This paper considers minimizing the $\ell_k$-norms of flow time on a single machine offline using a preemptive scheduler for $k\geq 1$. The objective is ideal for optimizing jobs' overall waiting times while simultaneously being fair to individual jobs. This work gives the first $O(1)$-approximation for the problem, improving

    更新日期:2020-06-30
  • Turning Big Data Into Tiny Data: Constant-Size Coresets for $k$-Means, PCA, and Projective Clustering
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-06-16
    Dan Feldman; Melanie Schmidt; Christian Sohler

    SIAM Journal on Computing, Volume 49, Issue 3, Page 601-657, January 2020. We develop and analyze a method to reduce the size of a very large set of data points in a high-dimensional Euclidean space $\mathbb{R}^d$ to a small set of weighted points such that the result of a predetermined data analysis task on the reduced set is approximately the same as that for the original point set. For example,

    更新日期:2020-06-30
  • On Locality-Sensitive Orderings and Their Applications
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-06-09
    Timothy M. Chan; Sariel Har-Peled; Mitchell Jones

    SIAM Journal on Computing, Volume 49, Issue 3, Page 583-600, January 2020. For any constant $d$ and parameter $\varepsilon \in (0,1/2]$, we show the existence of (roughly) $1/\varepsilon^d$ orderings on the unit cube $[0,1)^d$ such that for any two points $p, q\in [0,1)^d$ close together under the Euclidean metric, there is a linear ordering in which all points between $p$ and $q$ in the ordering are

    更新日期:2020-06-30
  • Prophet Inequalities Made Easy: Stochastic Optimization by Pricing Nonstochastic Inputs
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-06-02
    Paul Dütting; Michal Feldman; Thomas Kesselheim; Brendan Lucier

    SIAM Journal on Computing, Volume 49, Issue 3, Page 540-582, January 2020. We present a general framework for stochastic online maximization problems with combinatorial feasibility constraints. The framework establishes prophet inequalities by constructing price-based online approximation algorithms, a natural extension of threshold algorithms for settings beyond binary selection. Our analysis takes

    更新日期:2020-06-30
  • Distributed $(\Delta+1)$-Coloring via Ultrafast Graph Shattering
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-05-19
    Yi-Jun Chang; Wenzheng Li; Seth Pettie

    SIAM Journal on Computing, Volume 49, Issue 3, Page 497-539, January 2020. Vertex coloring is one of the classic symmetry breaking problems studied in distributed computing. In this paper, we present a new algorithm for $(\Delta+1)$-list coloring in the randomized ${LOCAL}$ model running in $O({Det}_{\scriptscriptstyle d}(\operatorname{poly} \log n))=O(\operatorname{poly}(\log\log n))$ time, where

    更新日期:2020-06-30
  • Spanoids---An Abstraction of Spanning Structures, and a Barrier for LCCs
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-05-13
    Zeev Dvir; Sivakanth Gopi; Yuzhou Gu; Avi Wigderson

    SIAM Journal on Computing, Volume 49, Issue 3, Page 465-496, January 2020. We introduce a simple logical inference structure we call a “spanoid" (generalizing the notion of a matroid), which captures well-studied problems in several areas. These include combinatorial geometry (point-line incidences), algebra (arrangements of hypersurfaces and ideals), statistical physics (bootstrap percolation), network

    更新日期:2020-06-30
  • Scheduling to Minimize Total Weighted Completion Time via Time-Indexed Linear Programming Relaxations
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-04-09
    Shi Li

    SIAM Journal on Computing, Ahead of Print. We study approximation algorithms for problems of scheduling precedence constrained jobs with the objective of minimizing total weighted completion time, in identical and related machine models. We give algorithms that improve upon many previous 15- to 20-year-old state-of-the-art results. A major theme in these results is the use of time-indexed linear programming

    更新日期:2020-04-09
  • The Greedy Spanner Is Existentially Optimal
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-04-09
    Arnold Filtser; Shay Solomon

    SIAM Journal on Computing, Volume 49, Issue 2, Page 429-447, January 2020. The greedy spanner is arguably the simplest and most well-studied spanner construction. Experimental results demonstrate that it is at least as good as any other spanner construction in terms of both the size and weight parameters. However, a rigorous proof for this statement has remained elusive. In this work we fill in the

    更新日期:2020-04-09
  • An Algorithmic Proof of the Lovász Local Lemma via Resampling Oracles
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-04-07
    Nicholas J. A. Harvey; Jan Vondrák

    SIAM Journal on Computing, Volume 49, Issue 2, Page 394-428, January 2020. The Lovász local lemma is a seminal result in probabilistic combinatorics. It gives a sufficient condition on a probability space and a collection of events for the existence of an outcome that simultaneously avoids all of those events. Finding such an outcome by an efficient algorithm has been an active research topic for decades

    更新日期:2020-04-07
  • Topology Is Irrelevant (In a Dichotomy Conjecture for Infinite Domain Constraint Satisfaction Problems)
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-03-30
    Libor Barto; Michael Pinsker

    SIAM Journal on Computing, Volume 49, Issue 2, Page 365-393, January 2020. The tractability conjecture for finite domain constraint satisfaction problems (CSPs) stated that such CSPs are solvable in polynomial time whenever there is no natural reduction, in some precise technical sense, from the 3-SAT problem; otherwise, they are NP-complete. Its recent resolution draws on an algebraic characterization

    更新日期:2020-03-30
  • Tight Bounds for Planar Strongly Connected Steiner Subgraph with Fixed Number of Terminals (and Extensions)
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-03-25
    Rajesh H. Chitnis; Andreas E. Feldmann; MohammadTaghi HajiAghayi; Daniel Marx

    SIAM Journal on Computing, Volume 49, Issue 2, Page 318-364, January 2020. Given a vertex-weighted directed graph $G=(V,E)$ and a set $T=\{t_1, t_2, \ldots, t_k\}$ of $k$ terminals, the objective of the Strongly Connected Steiner Subgraph (SCSS) problem is to find a vertex set $H\subseteq V$ of minimum weight such that $G[H]$ contains a $t_{i}\rightarrow t_j$ path for each $i\neq j$. The problem is

    更新日期:2020-03-25
  • Robust Positioning Patterns with Low Redundancy
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-03-23
    Yeow Meng Chee; Duc Tu Dao; Han Mao Kiah; San Ling; Hengjia Wei

    SIAM Journal on Computing, Volume 49, Issue 2, Page 284-317, January 2020. A robust positioning pattern is a large array that allows a mobile device to locate its position by reading a possibly corrupted small window around it. In this paper, we provide constructions of binary positioning patterns, equipped with efficient locating algorithms, that are robust to a constant number of errors and have

    更新日期:2020-03-23
  • Crossing the Logarithmic Barrier for Dynamic Boolean Data Structure Lower Bounds
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-03-12
    Kasper Green Larsen; Omri Weinstein; Huacheng Yu

    SIAM Journal on Computing, Ahead of Print. This paper proves the first superlogarithmic lower bounds on the cell probe complexity of dynamic Boolean (also known as decision) data structure problems, a long-standing milestone in data structure lower bounds. We introduce a new method for proving dynamic cell probe lower bounds and use it to prove an $\tilde{\Omega}({lg}^{1.5} \ n)$ lower bound on the

    更新日期:2020-03-12
  • Determinant-Preserving Sparsification of SDDM Matrices
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-03-10
    David Durfee; John Peebles; Richard Peng; Anup B. Rao

    SIAM Journal on Computing, Ahead of Print. We show that variants of spectral sparsification routines can preserve the total spanning tree counts of graphs. By Kirchhoff's matrix-tree theorem, this is equivalent to preserving the determinant of a graph Laplacian minor or, equivalently, of any symmetric diagonally dominant matrix (SDDM). Our analyses utilize this combinatorial connection to bridge the

    更新日期:2020-03-10
  • Zero-Knowledge Proof Systems for QMA
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-03-10
    Anne Broadbent; Zhengfeng Ji; Fang Song; John Watrous

    SIAM Journal on Computing, Volume 49, Issue 2, Page 245-283, January 2020. Prior work has established that all problems in NP admit classical zero-knowledge proof systems, and under reasonable hardness assumptions for quantum computations, these proof systems can be made secure against quantum attacks. We prove a result representing a further quantum generalization of this fact, which is that every

    更新日期:2020-03-10
  • Circuit Lower Bounds for Nondeterministic Quasi-polytime from a New Easy Witness Lemma
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-03-05
    Cody D. Murray; R. Ryan Williams

    SIAM Journal on Computing, Ahead of Print. We prove that if every problem in ${NP}$ has $n^k$-size circuits for a fixed constant $k$, then for every ${NP}$-verifier and every yes-instance $x$ of length $n$ for that verifier, the verifier's search space has an $n^{O(k^3)}$-size witness circuit: A witness for $x$ that can be encoded with a circuit of only $n^{O(k^3)}$ size. An analogous statement is

    更新日期:2020-03-05
  • Beating the Integrality Ratio for $s$-$t$-Tours in Graphs
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-02-27
    Vera Traub; Jens Vygen

    SIAM Journal on Computing, Ahead of Print. Among various variants of the traveling salesman problem (TSP), the $s$-$t$-path graph TSP has the special feature that we know the exact integrality ratio, $\frac{3}{2}$, and an approximation algorithm matching this ratio. In this paper, we go below this threshold: we devise a polynomial-time algorithm for the $s$-$t$-path graph TSP with approximation ratio

    更新日期:2020-02-27
  • Communication Complexity of Discrete Fair Division
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-02-27
    Benjamin Plaut; Tim Roughgarden

    SIAM Journal on Computing, Volume 49, Issue 1, Page 206-243, January 2020. We initiate the study of the communication complexity of fair division with indivisible goods. We focus on some of the most well studied fairness notions (envy-freeness, proportionality, and approximations thereof) and valuation classes (submodular, subadditive, and unrestricted). We show that for more than two players (and

    更新日期:2020-02-27
  • A Faster Isomorphism Test for Graphs of Small Degree
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-02-19
    Martin Grohe; Daniel Neuen; Pascal Schweitzer

    SIAM Journal on Computing, Ahead of Print. In a recent breakthrough, Babai [Proceedings of STOC, ACM, New York, 2016, pp. 684--697] gave a quasipolynomial-time graph isomorphism test. In this work, we give an improved isomorphism test for graphs of small degree: our algorithm runs in time $n^{\mathcal{O}((\log d)^{c})}$, where $n$ is the number of vertices of the input graphs, $d$ is the maximum degree

    更新日期:2020-02-19
  • Hardness Results for Structured Linear Systems
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-02-18
    Rasmus Kyng; Peng Zhang

    SIAM Journal on Computing, Ahead of Print. We show that if the nearly linear time solvers for Laplacian matrices and their generalizations can be extended to solve just slightly larger families of linear systems, then they can be used to quickly solve all systems of linear equations over the reals. This result can be viewed either positively or negatively: either nearly linear time algorithms can be

    更新日期:2020-02-18
  • Pseudorandom Pseudo-distributions with Near-Optimal Error for Read-Once Branching Programs
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-02-18
    Mark Braverman; Gil Cohen; Sumegha Garg

    SIAM Journal on Computing, Ahead of Print. Nisan [Combinatorica, 12 (1992), pp. 449--461] constructed a pseudorandom generator for length $n$, width $n$ read-once branching programs (ROBPs) with error $\varepsilon$ and seed length $O(\log^2{n} + \log{n} \cdot \log(1/\varepsilon))$. A major goal in complexity theory is to reduce the seed length, hopefully, to the optimal $O(\log{n}+\log(1/\varepsilon))$

    更新日期:2020-02-18
  • Approximation Limitations of Pure Dynamic Programming
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-02-18
    Stasys Jukna; Hannes Seiwert

    SIAM Journal on Computing, Volume 49, Issue 1, Page 170-205, January 2020. We prove the first, even superpolynomial, lower bounds on the size of tropical (min,+) and (max,+) circuits approximating given optimization problems. Many classical dynamic programming (DP) algorithms for optimization problems are pure in that they only use the basic $\min$, $\max$, $+$ operations in their recursion equations

    更新日期:2020-02-18
  • The Minimum Euclidean-Norm Point in a Convex Polytope: Wolfe's Combinatorial Algorithm is Exponential
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-02-18
    Jesús A. De Loera; Jamie Haddock; Luis Rademacher

    SIAM Journal on Computing, Volume 49, Issue 1, Page 138-169, January 2020. The complexity of Philip Wolfe's method for the minimum Euclidean-norm point problem over a convex polytope has remained unknown since he proposed the method in 1974. The method is important because it is used as a subroutine for one of the most practical algorithms for submodular function minimization. We present the first

    更新日期:2020-02-18
  • Sampling Lower Bounds: Boolean Average-Case and Permutations
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-02-18
    Emanuele Viola

    SIAM Journal on Computing, Volume 49, Issue 1, Page 119-137, January 2020. We show that for every small AC$^{0}$ circuit $C:\{0,1\}^{\ell}\to\{0,1\}^{m}$ there exists a multiset $S$ of $2^{m-m^{\Omega(1)}}$ restrictions that preserve the output distribution of $C$ and, moreover, polarize min-entropy: the restriction of $C$ to any $r\in S$ either is constant or has polynomial min-entropy. This structural

    更新日期:2020-02-18
  • Supercritical Space-Width Trade-offs for Resolution
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-02-04
    Christoph Berkholz; Jakob Nordström

    SIAM Journal on Computing, Volume 49, Issue 1, Page 98-118, January 2020. We show that there are CNF formulas which can be refuted in resolution in both small space and small width, but for which any small-width proof must have space exceeding by far the linear worst-case upper bound. This significantly strengthens the space-width trade-offs in [E. Ben-Sasson, SIAM J. Comput., 38 (2009), pp. 2511--2525]

    更新日期:2020-02-04
  • Approximate Modularity Revisited
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-01-21
    Uriel Feige; Michal Feldman; Inbal Talgam-Cohen

    SIAM Journal on Computing, Volume 49, Issue 1, Page 67-97, January 2020. Set functions with convenient properties (such as submodularity) appear in application areas of current interest, such as algorithmic game theory, and allow for improved optimization algorithms. It is natural to ask (e.g., in the context of data driven optimization) how robust such properties are, and whether small deviations

    更新日期:2020-01-21
  • Two-Round and Non-Interactive Concurrent Non-Malleable Commitments from Time-Lock Puzzles
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-01-16
    Huijia Lin; Rafael Pass; Pratik Soni

    SIAM Journal on Computing, Ahead of Print. Non-malleable commitments are a fundamental cryptographic tool for preventing (concurrent) man-in-the-middle attacks. Since their invention by Dolev, Dwork, and Naor in 1991, their round-complexity has been extensively studied, leading up to constant-round protocols based on one-way functions (OWFs), and three-round protocols based on sub-exponential OWFs

    更新日期:2020-01-16
  • Deciding Parity Games in Quasi-polynomial Time
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-01-14
    Cristian S. Calude; Sanjay Jain; Bakhadyr Khoussainov; Wei Li; Frank Stephan

    SIAM Journal on Computing, Ahead of Print. It is shown that the parity game can be solved in quasi-polynomial time. The parameterized parity game---with $n$ nodes and $m$ distinct values (a.k.a. colors or priorities)---is proven to be in the class of fixed parameter tractable problems when parameterized over $m$. Both results improve known bounds, from runtime $n^{O(\sqrt{n})}$ to $O(n^{\log(m)+6})$

    更新日期:2020-01-14
  • Hallucination Helps: Energy Efficient Virtual Circuit Routing
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-01-14
    Antonios Antoniadis; Sungjin Im; Ravishankar Krishnaswamy; Benjamin Moseley; Viswanath Nagarajan; Kirk Pruhs; Clifford Stein

    SIAM Journal on Computing, Volume 49, Issue 1, Page 37-66, January 2020. We consider virtual circuit routing protocols with an objective of minimizing energy in a network of components that are speed scalable, and that may be shut down when idle. We assume the standard model for component power: the power consumed by a component with load (speed) $s$ is $\sigma+ s^\alpha$, where $\sigma$ is the static

    更新日期:2020-01-14
  • Local Flow Partitioning for Faster Edge Connectivity
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-01-07
    Monika Henzinger; Satish Rao; Di Wang

    SIAM Journal on Computing, Volume 49, Issue 1, Page 1-36, January 2020. We study the problem of computing a minimum cut in a simple, undirected graph and give a deterministic $O(m \log^2 n \log\log^2 n)$ time algorithm. This improves on both the best previously known deterministic running time of $O(m \log^{12} n)$ (Kawarabayashi and Thorup [J. ACM, 66 (2018), 4]) and the best previously known randomized

    更新日期:2020-01-07
  • Collusion Resistant Traitor Tracing from Learning with Errors
    SIAM J. Comput. (IF 1.266) Pub Date : 2019-11-05
    Rishab Goyal; Venkata Koppula; Brent Waters

    SIAM Journal on Computing, Ahead of Print. In this work we provide a traitor tracing construction with ciphertexts that grow polynomially in $\log(n)$, where $n$ is the number of users, and prove it secure under the learning with errors (LWE) assumption. This is the first traitor tracing scheme with such parameters provably secure from a standard assumption. In addition to achieving new traitor tracing

    更新日期:2019-11-05
  • Smooth Heaps and a Dual View of Self-Adjusting Data Structures
    SIAM J. Comput. (IF 1.266) Pub Date : 2019-11-05
    László Kozma; Thatchaphol Saranurak

    SIAM Journal on Computing, Ahead of Print. We present a new connection between self-adjusting binary search trees (BSTs) and heaps, two fundamental, extensively studied, and practically relevant families of data structures [B. Allen and I. Munro, J. ACM, 25 (1978), pp. 526--535; D. D. Sleator and R. E. Tarjan, J. ACM, 32 (1985), pp. 652--686; M. L. Fredman et al., Algorithmica, 1 (1986), pp. 111--129;

    更新日期:2019-11-05
  • Round Compression for Parallel Matching Algorithms
    SIAM J. Comput. (IF 1.266) Pub Date : 2019-11-05
    Artur Czumaj; Jakub Ła̧cki; Aleksander Ma̧dry; Slobodan Mitrović; Krzysztof Onak; Piotr Sankowski

    SIAM Journal on Computing, Ahead of Print. For over a decade now we have been witnessing the success of massive parallel computation frameworks, such as MapReduce, Hadoop, Dryad, or Spark. Compared to the classic distributed algorithms or PRAM models, these frameworks allow for much more local computation. The fundamental question that arises however in this context is can we leverage this additional

    更新日期:2019-11-05
  • Holographic Algorithm with Matchgates Is Universal for Planar #CSP over Boolean Domain
    SIAM J. Comput. (IF 1.266) Pub Date : 2019-11-05
    Jin-Yi Cai; Zhiguo Fu

    SIAM Journal on Computing, Ahead of Print. We prove a complexity classification theorem that classifies all counting constraint satisfaction problems (#CSP) over Boolean variables into exactly three classes: (1) polynomial-time solvable; (2) #P-hard for general instances but solvable in polynomial time over planar structures; and (3) #P-hard over planar structures. The classification applies to all

    更新日期:2019-11-05
  • An Efficient Reduction from Two-Source to Nonmalleable Extractors: Achieving Near-Logarithmic Min-Entropy
    SIAM J. Comput. (IF 1.266) Pub Date : 2019-11-05
    Avraham Ben-Aroya; Dean Doron; Amnon Ta-Shma

    SIAM Journal on Computing, Ahead of Print. The breakthrough result of Chattopadhyay and Zuckerman [Explicit two-source extractors and resilient functions, in Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing (STOC), ACM, 2016, pp. 670--683] gives a reduction from the construction of explicit two-source extractors to the construction of explicit nonmalleable extractors. However

    更新日期:2019-11-05
  • Short Presburger Arithmetic Is Hard
    SIAM J. Comput. (IF 1.266) Pub Date : 2019-11-05
    Danny Nguyen; Igor Pak

    SIAM Journal on Computing, Ahead of Print. 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

    更新日期:2019-11-05
  • Tight Bounds for Single-Pass Streaming Complexity of the Set Cover Problem
    SIAM J. Comput. (IF 1.266) Pub Date : 2019-10-24
    Sepehr Assadi; Sanjeev Khanna; Yang Li

    SIAM Journal on Computing, Ahead of Print. We resolve the space complexity of single-pass streaming algorithms for approximating the classic set cover problem. For finding an $\alpha$-approximate set cover (for any $\alpha=o(\sqrt{n}/\log n)$) using a single-pass streaming algorithm, we show that $\Theta(mn/\alpha)$ space is both sufficient and necessary (up to an $O(\log n)$ factor); here $m$ denotes

    更新日期:2019-10-24
  • Constant-Round Interactive Proofs for Delegating Computation
    SIAM J. Comput. (IF 1.266) Pub Date : 2019-10-24
    Omer Reingold; Guy N. Rothblum; Ron D. Rothblum

    SIAM Journal on Computing, Ahead of Print. The celebrated ${\sf IP}={\sf PSPACE}$ theorem [Lund, Fortnow, Karloff, and Nisan, J. ACM, 39 (1992), pp. 859--868; Shamir, J. ACM, 39 (1992), pp. 869--877] allows an all-powerful but untrusted prover to convince a polynomial-time verifier of the validity of extremely complicated statements (as long as they can be evaluated using polynomial space). The interactive

    更新日期:2019-10-24
  • Exponential Separation of Communication and External Information
    SIAM J. Comput. (IF 1.266) Pub Date : 2019-10-24
    Anat Ganor; Gillat Kol; Ran Raz

    SIAM Journal on Computing, Ahead of Print. We show an exponential gap between communication complexity and external information complexity by analyzing a communication task suggested as a candidate by Braverman [A Hard-to-Compress Interactive Task?, in Proceedings of the 51th Annual Allerton Conference on Communication, Control, and Computing, IEEE, 2013]. Previously, only a separation of communication

    更新日期:2019-10-24
  • Bipartite Perfect Matching is in Quasi-NC
    SIAM J. Comput. (IF 1.266) Pub Date : 2019-10-24
    Stephen Fenner; Rohit Gurjar; Thomas Thierauf

    SIAM Journal on Computing, Ahead of Print. We show that the bipartite perfect matching problem is in quasi-$\mathsf{NC}^2$. That is, it has uniform circuits of quasi-polynomial size $n^{O(\log n)}$, and $O(\log^2 n)$ depth. Previously, only an exponential upper bound was known on the size of such circuits with poly-logarithmic depth. We obtain our result by an almost complete derandomization of the

    更新日期:2019-10-24
  • A (1+epsilon)-Approximation for Makespan Scheduling with Precedence Constraints Using LP Hierarchies
    SIAM J. Comput. (IF 1.266) Pub Date : 2019-10-24
    Elaine Levey; Thomas Rothvoss

    SIAM Journal on Computing, Ahead of Print. In a classical problem in scheduling, one has $n$ unit size jobs with a precedence order and the goal is to find a schedule of those jobs on $m$ identical machines as to minimize the makespan. It is one of the remaining four open problems from the book of Garey and Johnson whether or not this problem is $\mathbf{NP}$-hard for $m=3$. We prove that for any fixed

    更新日期:2019-10-24
  • A Duality-Based Unified Approach to Bayesian Mechanism Design
    SIAM J. Comput. (IF 1.266) Pub Date : 2019-10-24
    Yang Cai; Nikhil R. Devanur; S. Matthew Weinberg

    SIAM Journal on Computing, Ahead of Print. We provide a unified view of many recent developments in Bayesian mechanism design, including the black-box reductions of Cai, Daskalakis, and Weinberg [in Proceedings of the 54th Annual IEEE Symposium on Foundations of Computer Science, 2013], simple auctions for additive buyers [S. Hart and N. Nisan, in Proceedings of the 13th ACM Conference on Electronic

    更新日期:2019-10-24
  • Lift-and-Round to Improve Weighted Completion Time on Unrelated Machines
    SIAM J. Comput. (IF 1.266) Pub Date : 2019-10-24
    Nikhil Bansal; Aravind Srinivasan; Ola Svensson

    SIAM Journal on Computing, Ahead of Print. We consider the problem of scheduling jobs on unrelated machines so as to minimize the sum of weighted completion times. Our main result is a $(\nicefrac{3}{2}-c)$-approximation algorithm for some fixed $c>0$, improving upon the long-standing bound of $\nicefrac{3}{2}$. To do this, we first introduce a new lift-and-project-based SDP relaxation for the problem

    更新日期:2019-10-24
  • Local List Recovery of High-Rate Tensor Codes and Applications
    SIAM J. Comput. (IF 1.266) Pub Date : 2019-10-22
    Brett Hemenway; Noga Ron-Zewi; Mary Wootters

    SIAM Journal on Computing, Ahead of Print. We show that the tensor product of a high-rate globally list recoverable code is (approximately) locally list recoverable. List recovery has been a useful building block in the design of list decodable codes, and our motivation is to use the tensor construction as such a building block. In particular, instantiating this construction with known constructions

    更新日期:2019-10-22
  • Better Guarantees for $k$-Means and Euclidean $k$-Median by Primal-Dual Algorithms
    SIAM J. Comput. (IF 1.266) Pub Date : 2019-10-22
    Sara Ahmadian; Ashkan Norouzi-Fard; Ola Svensson; Justin Ward

    SIAM Journal on Computing, Ahead of Print. 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 in Euclidean space with a provable guarantee is a simple local search heuristic yielding an approximation guarantee of $9+\epsilon$, a ratio that is known to be

    更新日期:2019-10-22
  • A Nearly Optimal Lower Bound on the Approximate Degree of AC$^0$
    SIAM J. Comput. (IF 1.266) Pub Date : 2019-10-22
    Mark Bun; Justin Thaler

    SIAM Journal on Computing, Ahead of Print. The approximate degree of a Boolean function $f \colon \{-1, 1\}^n \rightarrow \{-1, 1\}$ 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

    更新日期:2019-10-22
  • On the Power of Statistical Zero Knowledge
    SIAM J. Comput. (IF 1.266) Pub Date : 2019-10-22
    Adam Bouland; Lijie Chen; Dhiraj Holden; Justin Thaler; Prashant Nalini Vasudevan

    SIAM Journal on Computing, Ahead of Print. We examine the power of statistical zero knowledge proofs (captured by the complexity class $SZK$) and their variants. First, we give the strongest known relativized evidence that $SZK$ contains hard problems, by exhibiting an oracle relative to which $SZK$ (indeed, even $NISZK$) is not contained in the class $UPP$, containing those problems solvable by randomized

    更新日期:2019-10-22
  • A Deterministic Almost-Tight Distributed Algorithm for Approximating Single-Source Shortest Paths
    SIAM J. Comput. (IF 1.266) Pub Date : 2019-10-21
    Monika Henzinger; Sebastian Krinninger; Danupon Nanongkai

    SIAM Journal on Computing, Ahead of Print. We present a deterministic $(1+o(1))$-approximation $(n^{1/2+o(1)}+D^{1+o(1)})$-time algorithm for solving the single-source shortest paths problem on distributed weighted networks (the \sf CONGEST model); here $n$ is the number of nodes in the network, $D$ is its (hop) diameter, and edge weights are positive integers from 1 to $\operatorname{poly}(n)$. This

    更新日期:2019-10-21
  • Algorithmic Bayesian Persuasion
    SIAM J. Comput. (IF 1.266) Pub Date : 2019-10-21
    Shaddin Dughmi; Haifeng Xu

    SIAM Journal on Computing, Ahead of Print. Persuasion, defined as the act of exploiting an informational advantage in order to influence the decisions of others, is ubiquitous. Indeed, persuasive communication has been estimated to account for almost a third of all economic activity in the U.S. This paper examines persuasion through a computational lens, focusing on what is perhaps the most basic and

    更新日期:2019-10-21
  • Two-Source Dispersers for Polylogarithmic Entropy and Improved Ramsey Graphs
    SIAM J. Comput. (IF 1.266) Pub Date : 2019-10-21
    Gil Cohen

    SIAM Journal on Computing, Ahead of Print. In his 1947 paper that inaugurated the probabilistic method, Erdös proved the existence of $(2+o(1))\log{n}$-Ramsey graphs on $n$ vertices. Matching Erdös's result with a constructive proof is considered a central problem in combinatorics and has gained significant attention in the literature. The state-of-the-art result was obtained in the celebrated paper

    更新日期:2019-10-21
  • A Tight Space Bound for Consensus
    SIAM J. Comput. (IF 1.266) Pub Date : 2019-10-21
    Leqi Zhu

    SIAM Journal on Computing, Ahead of Print. In the consensus problem, there are $n$ processes that each has a private input value. Each nonfaulty process must output a single value such that no two processes output different values and the output is the input value of some process. There are many consensus protocols for systems where the processes may only communicate by reading and writing to shared

    更新日期:2019-10-21
  • Breaking the Logarithmic Barrier for Truthful Combinatorial Auctions with Submodular Bidders
    SIAM J. Comput. (IF 1.266) Pub Date : 2019-10-21
    Shahar Dobzinski

    SIAM Journal on Computing, Ahead of Print. We study a central problem in algorithmic mechanism design: constructing truthful mechanisms for welfare maximization in combinatorial auctions with submodular bidders. Dobzinski, Nisan, and Schapira provided the first mechanism that guarantees a nontrivial approximation ratio of $O(\log^2 m)$ [STOC'06, ACM, New York, 2006, pp. 644--652], where $m$ is the

    更新日期:2019-10-21
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