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  • Algorithmic Polynomials
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-11-24
    Alexander A. Sherstov

    SIAM Journal on Computing, Volume 49, Issue 6, Page 1173-1231, January 2020. The approximate degree of a Boolean function $f(x_{1},x_{2},\ldots,x_{n})$ is the minimum degree of a real polynomial that approximates $f$ pointwise within $1/3$. Upper bounds on approximate degree have a variety of applications in learning theory, differential privacy, and algorithm design in general. Nearly all known upper

    更新日期:2020-11-25
  • Hardness of Continuous Local Search: Query Complexity and Cryptographic Lower Bounds
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-11-19
    Pavel Hubáček; Eylon Yogev

    SIAM Journal on Computing, Volume 49, Issue 6, Page 1128-1172, January 2020. Local search proved to be an extremely useful tool when facing hard optimization problems (e.g., via the simplex algorithm, simulated annealing, or genetic algorithms). Although powerful, it has its limitations: there are functions for which exponentially many queries are needed to find a local optimum. In many contexts, the

    更新日期:2020-11-21
  • Constructive Polynomial Partitioning for Algebraic Curves in $\mathbb{R}^3$ with Applications
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-11-12
    Boris Aronov; Esther Ezra; Joshua Zahl

    SIAM Journal on Computing, Volume 49, Issue 6, Page 1109-1127, January 2020. In 2015, Guth [Math. Proc. Cambridge Philos. Soc., 159 (2015), pp. 459--469] proved that for any set of $k$-dimensional bounded complexity varieties in ${\mathbb R}^d$ and for any positive integer $D$, there exists a polynomial of degree at most $D$ whose zero set divides ${\mathbb R}^d$ into open connected sets so that only

    更新日期:2020-11-15
  • Nearly Work-Efficient Parallel Algorithm for Digraph Reachability
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-10-22
    Jeremy T. Fineman

    SIAM Journal on Computing, Volume 49, Issue 5, Page STOC18-500-STOC18-539, January 2020. One of the simplest problems on directed graphs is that of identifying the set of vertices reachable from a designated source vertex. This problem can be solved easily sequentially by performing a graph search, but efficient parallel algorithms have eluded researchers for decades. For sparse high-diameter graphs

    更新日期:2020-11-12
  • A Friendly Smoothed Analysis of the Simplex Method
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-10-22
    Daniel Dadush; Sophie Huiberts

    SIAM Journal on Computing, Volume 49, Issue 5, Page STOC18-449-STOC18-499, January 2020. Explaining the excellent practical performance of the simplex method for linear programming has been a major topic of research for over 50 years. One of the most successful frameworks for understanding the simplex method was given by Spielman and Teng [J. ACM, 51 (2004), pp. 385--463] who developed the notion of

    更新日期:2020-11-12
  • Special Section on the Fiftieth Annual ACM Symposium on Theory of Computing (STOC 2018)
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-10-28
    Thomas Vidick; Danupon Nanongkai; Dimitris Achlioptas

    SIAM Journal on Computing, Volume 49, Issue 5, Page STOC18-i-STOC18-ii, January 2020. This issue of SICOMP contains 10 specially selected papers from the Fiftieth Annual ACM Symposium on Theory of Computing, otherwise known as STOC 2018, held June 25 to 29 in Los Angeles, California. The papers here were chosen to represent both the excellence and the broad range of the STOC program. The papers have

    更新日期:2020-11-12
  • Nonmalleable Extractors and Codes, with Their Many Tampered Extensions
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-10-20
    Eshan Chattopadhyay; Vipul Goyal; Xin Li

    SIAM Journal on Computing, Volume 49, Issue 5, Page 999-1040, January 2020. Randomness extractors and error correcting codes are fundamental objects in computer science. Recently, there have been several natural generalizations of these objects, in the context and study of tamper-resilient cryptography. These are seeded nonmalleable extractors, introduced by Dodis and Wichs (STOC 2009); seedless nonmalleable

    更新日期:2020-11-12
  • A Quasi-Polynomial Approximation for the Restricted Assignment Problem
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-11-03
    Klaus Jansen; Lars Rohwedder

    SIAM Journal on Computing, Volume 49, Issue 6, Page 1083-1108, January 2020. The Restricted Assignment problem is a prominent special case of Scheduling on Unrelated Parallel Machines. For the strongest known linear programming relaxation, the configuration LP, we improve the nonconstructive bound on its integrality gap from 1.9412 to 1.8334 and significantly simplify the proof. Then we give a constructive

    更新日期:2020-11-12
  • Computational Two-Party Correlation: A Dichotomy for Key-Agreement Protocols
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-11-03
    Iftach Haitner; Kobbi Nissim; Eran Omri; Ronen Shaltiel; Jad Silbak

    SIAM Journal on Computing, Volume 49, Issue 6, Page 1041-1082, January 2020. Let $\pi$ be an efficient two-party protocol that, given security parameter $\kappa$, both parties output single bits $X_\kappa$ and $Y_\kappa$, respectively. We are interested in how $(X_\kappa,Y_\kappa)$ “appears” to an efficient adversary that only views the transcript $T_\kappa$. We make the following contributions: (a)

    更新日期:2020-11-12
  • Amplification and Derandomization without Slowdown
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-10-08
    Ofer Grossman; Dana Moshkovitz

    SIAM Journal on Computing, Volume 49, Issue 5, Page 959-998, January 2020. We present techniques for decreasing the error probability of randomized algorithms and for converting randomized algorithms to deterministic (nonuniform) algorithms. Unlike most existing techniques that involve repetition of the randomized algorithm and hence a slowdown, our techniques produce algorithms with similar run-time

    更新日期:2020-10-14
  • Constant Factor Approximation Algorithm for Weighted Flow-Time on a Single Machine in PseudoPolynomial Time
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-09-29
    Jatin Batra; Naveen Garg; Amit Kumar

    SIAM Journal on Computing, Ahead of Print. In the weighted flow-time problem on a single machine, we are given a set of $n$ jobs, where each job has a processing requirement $p_j$, release date $r_j$, and weight $w_j$. The goal is to find a preemptive schedule which minimizes the sum of weighted flow-time of jobs, where the flow-time of a job is the difference between its completion time and its released

    更新日期:2020-09-30
  • Inapproximability of the Independent Set Polynomial in the Complex Plane
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-09-24
    Ivona Bezáková; Andreas Galanis; Leslie Ann Goldberg; Daniel Štefankovič

    SIAM Journal on Computing, Ahead of Print. We study the complexity of approximating the value of the independent set polynomial $Z_G(\lambda)$ of a graph $G$ with maximum degree $\Delta$ when the activity $\lambda$ is a complex number. When $\lambda$ is real, the complexity picture is well understood, and is captured by two real-valued thresholds $\lambda^*$ and $\lambda_c$, which depend on $\Delta$

    更新日期:2020-09-30
  • Tight Revenue Gaps Among Simple Mechanisms
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-09-09
    Yaonan Jin; Pinyan Lu; Zhihao Gavin Tang; Tao Xiao

    SIAM Journal on Computing, Volume 49, Issue 5, Page 927-958, January 2020. We consider a fundamental problem in microeconomics: selling a single item to a number of potential buyers, whose values are drawn from known independent and regular (not necessarily identical) distributions. There are four widely used and widely studied mechanisms in the literature: Myerson Auction (OPT), Sequential Posted-Pricing

    更新日期:2020-09-30
  • Query-to-Communication Lifting for BPP
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-08-12
    Mika Göös; Toniann Pitassi; Thomas Watson

    SIAM Journal on Computing, Volume 49, Issue 4, Page FOCS17-441-FOCS17-461, January 2020. For any $n$-bit boolean function $f$, we show that the randomized communication complexity of the composed function $f\circ g^n$, 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

    更新日期:2020-09-03
  • Special Section on the Fifty-Eighth Annual IEEE Symposium on Foundations of Computer Science (FOCS 2017)
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-08-18
    Valentine Kabanets; Sofya Raskhodnikova; Chaitanya Swamy

    SIAM Journal on Computing, Volume 49, Issue 4, Page FOCS17-i-FOCS17-i, January 2020. This special section comprises nine fully refereed papers whose extended abstracts were presented at the 58th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2017) in Berkeley, California, on October 15--17, 2017. The preliminary conference versions of these papers were published by in the FOCS 2017

    更新日期:2020-09-03
  • Find Your Place: Simple Distributed Algorithms for Community Detection
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-08-04
    Luca Becchetti; Andrea E. Clementi; Emanuele Natale; Francesco Pasquale; Luca Trevisan

    SIAM Journal on Computing, Volume 49, Issue 4, Page 821-864, January 2020. Given an underlying graph, we consider the following dynamics: Initially, each node locally chooses a value in $\{-1,1\}$, uniformly at random and independently of other nodes. Then, in each consecutive round, every node updates its local value to the average of the values held by its neighbors, at the same time applying an

    更新日期:2020-09-03
  • Simple Optimal Hitting Sets for Small-Success RL
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-07-30
    William M. Hoza; David Zuckerman

    SIAM Journal on Computing, Volume 49, Issue 4, Page 811-820, January 2020. We give a simple explicit hitting set generator for read-once branching programs of width $w$ and length $r$ with known variable order and acceptance probability at least $\epsilon$. When $r = w$, our generator has seed length $O(\log^2 r + \log(1/\epsilon))$. When $r = \text{polylog } w$, our generator has optimal seed length

    更新日期:2020-09-03
  • Strong Connectivity in Directed Graphs under Failures, with Applications
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-09-01
    Loukas Georgiadis; Giuseppe F. Italiano; Nikos Parotsidis

    SIAM Journal on Computing, Volume 49, Issue 5, Page 865-926, January 2020. In this paper, we investigate some basic connectivity problems in directed graphs (digraphs). Let $G$ be a digraph with $m$ edges and $n$ vertices, and let $G\setminus e$ (resp., $G\setminus v$) be the digraph obtained after deleting edge $e$ (resp., vertex $v$) from $G$. As a first result, we show how to compute in $O(m+n)$

    更新日期:2020-09-03
  • 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:2020-07-23
  • 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:2020-07-23
  • 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:2020-07-23
  • 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:2020-07-23
  • 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:2020-07-23
  • 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:2020-07-23
  • 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:2020-07-23
  • From Gap-Exponential Time Hypothesis to Fixed Parameter Tractable Inapproximability: Clique, Dominating Set, and More
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-07-21
    Parinya Chalermsook; Marek Cygan; Guy Kortsarz; Bundit Laekhanukit; Pasin Manurangsi; Danupon Nanongkai; Luca Trevisan

    SIAM Journal on Computing, Volume 49, Issue 4, Page 772-810, January 2020. We consider questions that arise from the intersection between the areas of polynomial-time approximation algorithms, subexponential-time algorithms, and fixed-parameter tractable (FPT) algorithms. The questions, which have been asked several times, are whether there is a nontrivial FPT-approximation algorithm for the Maximum

    更新日期:2020-07-23
  • On Approximating the Number of $k$-Cliques in Sublinear Time
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-07-14
    Talya Eden; Dana Ron; C. Seshadhri

    SIAM Journal on Computing, Volume 49, Issue 4, Page 747-771, January 2020. We study the problem of approximating the number of $k$-cliques in a graph when given query access to the graph. We consider the standard query model for general graphs via (1) degree queries, (2) neighbor queries, and (3) pair queries. Let $n$ denote the number of vertices in the graph, $m$ the number of edges, and $C_k$ the

    更新日期:2020-07-23
  • Distributed Local Approximation Algorithms for Maximum Matching in Graphs and Hypergraphs
    SIAM J. Comput. (IF 1.266) Pub Date : 2020-07-09
    David G. Harris

    SIAM Journal on Computing, Volume 49, Issue 4, Page 711-746, January 2020. We describe approximation algorithms in Linial's classic LOCAL model of distributed computing to find maximum-weight matchings in a hypergraph of rank $r$. Our main result is a deterministic algorithm to generate a matching which is an $O(r)$-approximation to the maximum- weight matching, running in $\tilde O(r \log \Delta +

    更新日期:2020-07-23
  • 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:2020-07-23
  • 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:2020-05-13
  • 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:2020-04-27
  • 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
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