• 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：2020-09-10
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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 $\tilde O(r \log \Delta + 更新日期：2020-07-23 • SIAM J. Comput. (IF 1.266) Pub Date : 2020-07-01 Matthew Jenssen; Peter Keevash; Will Perkins SIAM Journal on Computing, Volume 49, Issue 4, Page 681-710, January 2020. We give a fully polynomial-time approximation scheme (FPTAS) and an efficient sampling algorithm for the high-fugacity hard-core model on bounded-degree bipartite expander graphs and the low-temperature ferromagnetic Potts model on bounded-degree expander graphs. The results apply, for example, to random (bipartite)$\Delta$-regular 更新日期：2020-07-23 • SIAM J. Comput. (IF 1.266) Pub Date : 2020-05-13 Zeev Dvir; Sivakanth Gopi; Yuzhou Gu; Avi Wigderson SIAM Journal on Computing, Volume 49, Issue 3, Page 465-496, January 2020. We introduce a simple logical inference structure we call a “spanoid" (generalizing the notion of a matroid), which captures well-studied problems in several areas. These include combinatorial geometry (point-line incidences), algebra (arrangements of hypersurfaces and ideals), statistical physics (bootstrap percolation), network 更新日期：2020-05-13 • SIAM J. Comput. (IF 1.266) Pub Date : 2020-04-27 Jacob Fox; Tim Roughgarden; C. Seshadhri; Fan Wei; Nicole Wein SIAM Journal on Computing, Volume 49, Issue 2, Page 448-464, January 2020. We propose a new distribution-free model of social networks. Our definitions are motivated by one of the most universal signatures of social networks, triadic closure---the property that pairs of vertices with common neighbors tend to be adjacent. Our most basic definition is that of a$c$-closed graph, where for every pair 更新日期：2020-04-27 • 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 • 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 • 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 • 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 • 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$. The problem is 更新日期：2020-03-25 • SIAM J. Comput. (IF 1.266) Pub Date : 2020-03-23 Yeow Meng Chee; Duc Tu Dao; Han Mao Kiah; San Ling; Hengjia Wei SIAM Journal on Computing, Volume 49, Issue 2, Page 284-317, January 2020. A robust positioning pattern is a large array that allows a mobile device to locate its position by reading a possibly corrupted small window around it. In this paper, we provide constructions of binary positioning patterns, equipped with efficient locating algorithms, that are robust to a constant number of errors and have 更新日期：2020-03-23 • SIAM J. Comput. (IF 1.266) Pub Date : 2020-03-12 Kasper Green Larsen; Omri Weinstein; Huacheng Yu SIAM Journal on Computing, Ahead of Print. This paper proves the first superlogarithmic lower bounds on the cell probe complexity of dynamic Boolean (also known as decision) data structure problems, a long-standing milestone in data structure lower bounds. We introduce a new method for proving dynamic cell probe lower bounds and use it to prove an$\tilde{\Omega}({lg}^{1.5} \ n)$lower bound on the 更新日期：2020-03-12 • SIAM J. Comput. (IF 1.266) Pub Date : 2020-03-10 David Durfee; John Peebles; Richard Peng; Anup B. Rao SIAM Journal on Computing, Ahead of Print. We show that variants of spectral sparsification routines can preserve the total spanning tree counts of graphs. By Kirchhoff's matrix-tree theorem, this is equivalent to preserving the determinant of a graph Laplacian minor or, equivalently, of any symmetric diagonally dominant matrix (SDDM). Our analyses utilize this combinatorial connection to bridge the 更新日期：2020-03-10 • SIAM J. Comput. (IF 1.266) Pub Date : 2020-03-10 Anne Broadbent; Zhengfeng Ji; Fang Song; John Watrous SIAM Journal on Computing, Volume 49, Issue 2, Page 245-283, January 2020. Prior work has established that all problems in NP admit classical zero-knowledge proof systems, and under reasonable hardness assumptions for quantum computations, these proof systems can be made secure against quantum attacks. We prove a result representing a further quantum generalization of this fact, which is that every 更新日期：2020-03-10 • SIAM J. Comput. (IF 1.266) Pub Date : 2020-03-05 Cody D. Murray; R. Ryan Williams SIAM Journal on Computing, Ahead of Print. We prove that if every problem in${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)}$size. An analogous statement is 更新日期：2020-03-05 • SIAM J. Comput. (IF 1.266) Pub Date : 2020-02-27 Vera Traub; Jens Vygen SIAM Journal on Computing, Ahead of Print. Among various variants of the traveling salesman problem (TSP), the$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$-path graph TSP with approximation ratio 更新日期：2020-02-27 • SIAM J. Comput. (IF 1.266) Pub Date : 2020-02-27 Benjamin Plaut; Tim Roughgarden SIAM Journal on Computing, Volume 49, Issue 1, Page 206-243, January 2020. We initiate the study of the communication complexity of fair division with indivisible goods. We focus on some of the most well studied fairness notions (envy-freeness, proportionality, and approximations thereof) and valuation classes (submodular, subadditive, and unrestricted). We show that for more than two players (and 更新日期：2020-02-27 • SIAM J. Comput. (IF 1.266) Pub Date : 2020-02-19 Martin Grohe; Daniel Neuen; Pascal Schweitzer SIAM Journal on Computing, Ahead of Print. In a recent breakthrough, Babai [Proceedings of STOC, ACM, New York, 2016, pp. 684--697] gave a quasipolynomial-time graph isomorphism test. In this work, we give an improved isomorphism test for graphs of small degree: our algorithm runs in time$n^{\mathcal{O}((\log d)^{c})}$, where$n$is the number of vertices of the input graphs,$d$is the maximum degree 更新日期：2020-02-19 • SIAM J. Comput. (IF 1.266) Pub Date : 2020-02-18 Rasmus Kyng; Peng Zhang SIAM Journal on Computing, Ahead of Print. We show that if the nearly linear time solvers for Laplacian matrices and their generalizations can be extended to solve just slightly larger families of linear systems, then they can be used to quickly solve all systems of linear equations over the reals. This result can be viewed either positively or negatively: either nearly linear time algorithms can be 更新日期：2020-02-18 • SIAM J. Comput. (IF 1.266) Pub Date : 2020-02-18 Mark Braverman; Gil Cohen; Sumegha Garg SIAM Journal on Computing, Ahead of Print. Nisan [Combinatorica, 12 (1992), pp. 449--461] constructed a pseudorandom generator for length$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))$更新日期：2020-02-18 • SIAM J. Comput. (IF 1.266) Pub Date : 2020-02-18 Stasys Jukna; Hannes Seiwert SIAM Journal on Computing, Volume 49, Issue 1, Page 170-205, January 2020. We prove the first, even superpolynomial, lower bounds on the size of tropical (min,+) and (max,+) circuits approximating given optimization problems. Many classical dynamic programming (DP) algorithms for optimization problems are pure in that they only use the basic$\min$,$\max$,$+$operations in their recursion equations 更新日期：2020-02-18 • SIAM J. Comput. (IF 1.266) Pub Date : 2020-02-18 Jesús A. De Loera; Jamie Haddock; Luis Rademacher SIAM Journal on Computing, Volume 49, Issue 1, Page 138-169, January 2020. The complexity of Philip Wolfe's method for the minimum Euclidean-norm point problem over a convex polytope has remained unknown since he proposed the method in 1974. The method is important because it is used as a subroutine for one of the most practical algorithms for submodular function minimization. We present the first 更新日期：2020-02-18 • SIAM J. Comput. (IF 1.266) Pub Date : 2020-02-18 Emanuele Viola SIAM Journal on Computing, Volume 49, Issue 1, Page 119-137, January 2020. We show that for every small AC$^{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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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
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