SIAM Journal on Computing, Volume 50, Issue 3, Page STOC16-i-STOC16-iii, January 2021.
This issue of SICOMP contains 14 specially selected papers from the 48th Annual ACM Symposium on Theory of Computing (STOC 2016), held June 18--June 21, 2016, in Cambridge, Massachusetts. The papers here were chosen to represent both the excellence and the broad range of the STOC program. The papers have been revised and extended by the authors and subjected to the standard thorough reviewing process of SICOMP. The program committee members were Alexandr Andoni, Sanjeev Arora, Allison Bishop, Avrim Blum, Keren Censor-Hillel, Timothy Chan, Chandra Chekuri, Jing Chen, Zeev Dvir, Fabrizio Grandoni, Parikshit Gopalan, Kasper Green Larsen, Huijia (Rachel) Lin, Konstantin Makarychev, Yishay Mansour (chair), Jakob Nordström, Debmalya Panigrahi, Prasad Raghavendra, Sofya Raskhodnikova, R Ravi, Mario Szegedy, Êva Tardos, Salil Vadhan, Avi Wigderson, and Ronald de Wolf. We briefly describe here the papers that appear in this special issue. In “Breaking the Logarithmic Barrier for Truthful Combinatorial Auctions with Submodular Bidders,” Shahar Dobzinski provides the first truthful mechanism for welfare maximization in combinatorial auctions with submodular bidders whose approximation ratio is $O(\sqrt{\log m})$. Previously the best ratio was $O(\log m)$. In “A Tight Space Bound for Consensus,” Leqi Zhu proves that every randomized wait-free (or obstruction-free) consensus protocol for $n$ processes must use at least $n-1$ registers. Previously, this bound was known only in the anonymous setting, while for the general case only a $\sqrt{n}$ bound was known. In “Two-Source Dispersers for Polylogarithmic Entropy and Improved Ramsey Graphs,” Gil Cohen constructs a $2^{(\log\log n)^c}$-Ramsey graph for some universal constant $c$, a significant improvement in this direction. In the language of theoretical computer science, this resolves the problem of explicitly constructing dispersers for two $n$-bit sources with entropy ${polylog}(n)$. Previously, such dispersers could only support entropy $\Omega(n)$. In “Algorithmic Bayesian Persuasion,” Shaddin Dughmi and Haifeng Xu examines Bayesian persuasion through a computational lens for the first time. When the payoff distributions are i.i.d. across actions, the authors provide a polynomial-time optimal solution and a “simple” $(1-1/e)$-approximation. For independent but nonidentical distributions, \#P-hardness is proved. For the general case with a black-box sampling oracle, an FPTAS is provided and shown to be the best possible under the black-box model. In “A Deterministic Almost-Tight Distributed Algorithm for Approximating Single-Source Shortest Paths,” Monika Henzinger, Sebastian Krinninger, and Danupon Nanongkai present a deterministic $(1 + o(1))$-approximation algorithm for solving the single-source shortest paths problem on distributed weighted networks in $O(n^{1/2+o(1)} + D^{1+o(1)})$ rounds, where $n$ is the number of nodes and $D$ is the diameter of the network. This improves upon previous results in being deterministic and completing in less time or in obtaining a smaller approximation factor. Moreover, it is almost tight due to a known lower bound. In “Lift-and-Round to Improve Weighted Completion Time on Unrelated Machines,” Nikhil Bansal, Aravind Srinivasan, and Ola Svensson improve, by a small but fixed constant, the long-standing approximation factor of $3/2$ for the problem of scheduling jobs on unrelated machines so as to minimize the sum of weighted completion times. In “A Duality-Based Unified Approach to Bayesian Mechanism Design,” Yang Cai, Nikhil Devanur, and Seth Matthew Weinberg provide a duality-based unified framework for designing simple and approximately optimal auctions. Using this framework, the authors prove that either a posted-price mechanism or the Vickrey--Clarke--Groves auction with per-bidder entry fees achieves a constant-factor of the optimal revenue achievable by a Bayesian Incentive Compatible mechanism whenever buyers are unit-demand or additive, unifying previous breakthroughs of Chawla et al. and Yao, and improving both approximation ratios. In “A $(1+\varepsilon)$-Approximation for Makespan Scheduling with Precedence Constraints using LP Hierarchies,” Elaine Levey and Thomas Rothvoss consider the problem of scheduling $n$ unit size jobs with a precedence order on $m$ identical machines as to minimize the makespan. They prove that for any fixed $\epsilon$ and $m$, an LP-hierarchy lift of the time-indexed LP with a slightly super poly-logarithmic number of $r = (\log n)^{\Theta(\log \log n)}$ rounds provides a $(1 + \epsilon)$-approximation. The previous best approximation algorithms for this problem guarantee a $(2 - 7/(3m+1))$-approximation in polynomial time for $m \ge 4$ and $4/3$ for $m=3$. In “Bipartite Perfect Matching Is in Quasi-${{NC}}$,” Stephen Fenner, Rohit Gurjar, and Thomas Thierauf show that the bipartite perfect matching problem is in quasi-${{NC}}^2$. 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. In “Exponential Separation of Communication and External Information,” Anat Ganor, Gillat Kol, and Ran Raz prove the first gap, an exponential gap, between external information complexity and communication complexity of a communication task. Previously such a separation was known only for the internal information vs communication complexity. This result has implication to the question of compressing communication protocols to the amount of information they reveal about the inputs. In “Constant-Round Interactive Proofs for Delegating Computation,” Omer Reingold, Guy Rothblum, and Ron Rothblum design efficient, constant-round interactive proofs. They show that for any statement that can be evaluated in polynomial time and space $S$, there exists a constant-round interactive protocol where the prover has polynomial runtime and the verifier has a runtime of about $n+\poly(S)$. Prior to this work, very little was known about the power of constant-round protocol. This result is a major step for the grand challenge of verifiable delegation of computation. In “Tight Bounds for Single-Pass Streaming Complexity of the Set Cover Problem,” Sepehr Assadi, Sanjeev Khanna, and Yang Li 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 $\alpha= o(\sqrt{n})$) using a single-pass streaming algorithm, they show that $\Theta(mn/\alpha)$ space is both sufficient and necessary (up to an $O(\log n)$ factor), where $m$ denotes number of the sets and $n$ denotes size of the universe. They further study the problem of estimating the size of a minimum set cover (as opposed to finding the actual sets) and achieve an additional saving of a factor of $\alpha$ in the space complexity, which is also the best possible. In “A Polynomial Lower Bound for Testing Monotonicity,” Aleksandrs Belovs and Eric Blais show a polynomial lower bound on query complexity for adaptive testers of monotonicity of an $n$-variate Boolean function. Prior to this work, similar lower bounds were known only for the nonadaptive testers, and proving similar bounds for adaptive testers has been a major challenge. In “Algorithmic Stability for Adaptive Data Analysis,” Raef Bassily, Kobbi Nissim, Adam Smith, Thomas Steinke, Uri Stemmer, and Jonathan Ullman take a solid step forward in the area of adaptive data analysis by establishing a clean, tight connection between the notion of differential privacy (max-KL stability) and design of adaptive queries. This connection improves a number of bounds that were known prior to this paper, and generalizes to handle more “data analysis" settings. We thank the authors, the program committee members, and the reviewers for STOC 2016 for their hard work, and we especially thank the SICOMP reviewers for their work in evaluating submitted papers.

中文翻译：

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第 48 届 ACM 计算理论年会特别部分 (STOC 2016)

SIAM Journal on Computing，第 50 卷，第 3 期，第 STOC16-i-STOC16-iii 页，2021 年 1 月。
本期 SICOMP 收录了 2016 年 6 月 18 日至 6 月 21 日在马萨诸塞州剑桥举行的第 48 届 ACM 计算理论年会 (STOC 2016) 中精选的 14 篇论文。选择这里的论文来代表 STOC 计划的卓越性和广泛性。作者对论文进行了修订和扩展，并经过了 SICOMP 的标准彻底审查过程。程序委员会成员有 Alexandr Andoni、Sanjeev Arora、Allison Bishop、Avrim Blum、Keren Censor-Hillel、Timothy Chan、Chandra Chekuri、Jing Chen、Zeev Dvir、Fabrizio Grandoni、Parikshit Gopalan、Kasper Green Larsen、Huijia (Rachel) Lin、 Konstantin Makarychev、Yishay Mansour（主席）、Jakob Nordström、Debmalya Panigrahi、Prasad Raghavendra、Sofya Raskhodnikova、R Ravi、Mario Szegedy、Êva Tardos、Salil Vadhan、Avi Wigderson、和罗纳德·德·沃尔夫。我们在此简要介绍本期特刊中出现的论文。在“Breaking the Logarithmic Barrier for Truthful Combinatorial Auctions with Submodular Bidders”一文中，Shahar Dobzinski 提供了第一个真实的机制，用于在近似比率为 $O(\sqrt{\log m})$ 的子模块投标人的组合拍卖中实现福利最大化。以前最好的比率是 $O(\log m)$。在“A Tight Space Bound for Consensus”中，朱乐奇证明了每个用于 $n$ 进程的随机无等待（或无阻塞）共识协议必须至少使用 $n-1$ 个寄存器。以前，此界限仅在匿名设置中已知，而对于一般情况，只有 $\sqrt{n}$ 界限是已知的。在“多对数熵和改进拉姆齐图的双源分散器”中，” Gil Cohen 为某个通用常数 $c$ 构建了 $2^{(\log\log n)^c}$-Ramsey 图，在这个方向上有显着的改进。用理论计算机科学的语言来说，这解决了为两个 $n$ 位源的熵为 ${polylog}(n)$ 显式构造分散器的问题。以前，这种分散器只能支持熵 $\Omega(n)$。在“算法贝叶斯说服”中，Shaddin Dughmi 和 Haifeng Xu 首次通过计算镜头研究了贝叶斯说服。当收益分布在动作之间是 iid 时，作者提供了一个多项式时间最优解和一个“简单”的 $(1-1/e)$ 近似值。对于独立但不相同的分布，\#P-hardness 得到证明。对于黑盒采样预言机的一般情况，提供了一个 FPTAS，并证明在黑盒模型下是最好的。在“用于近似单源最短路径的确定性几乎紧分布式算法”中，Monika Henzinger、Sebastian Krinninger 和 Danupon Nanongkai 提出了一种确定性 $(1 + o(1))$-近似算法，用于求解单源最短路径$O(n^{1/2+o(1)} + D^{1+o(1)})$轮中分布式加权网络的路径问题，其中$n$是节点数，$D$是网络的直径。这在确定性和在更短的时间内完成或在获得更小的近似因子方面改进了先前的结果。此外，由于已知的下限，它几乎是紧的。在“提高无关机器的加权完成时间”中，Nikhil Bansal、Aravind Srinivasan 和 Ola Svensson 改进了，通过一个小但固定的常数，长期存在的近似因子 $3/2$ 用于在不相关的机器上调度作业的问题，以便最小化加权完成时间的总和。在“A Duality-Based Unified Approach to Bayesian Mechanism Design”中，Yang Cai、Nikhil Devanur 和 Seth Matthew Weinberg 提供了一个基于对偶的统一框架，用于设计简单且近似最优的拍卖。使用这个框架，作者证明了无论是张贴价格机制还是 Vickrey--Clarke--Groves 拍卖，只要买方是单位-需求或添加剂，统一了 Chawla 等人先前的突破。和姚，并提高两个近似比率。在“A $(1+\varepsilon)$-Approximation for Makespan Scheduling with Precedence Constraints using LP Hierarchies”中，Elaine Levey 和 Thomas Rothvoss 考虑了在 $m$ 相同机器上以优先顺序调度 $n$ 单位大小作业的问题以尽量减少完工时间。他们证明，对于任何固定的 $\epsilon$ 和 $m$，时间索引 LP 的 LP 层次提升具有 $r = (\log n)^{\Theta(\log \log n)}$ rounds 提供了 $(1 + \epsilon)$ 近似值。之前针对这个问题的最佳近似算法保证了 $(2 - 7/(3m+1))$-对于 $m\ge 4$ 和 $4/3$ 对于 $m=3$ 在多项式时间内的近似值。在“Bipartite Perfect Matching Is in Quasi-${{NC}}$”中，Stephen Fenner、Rohit Gurjar 和 Thomas Thierauf 表明二部完美匹配问题在拟 ${{NC}}^2$ 中。那是，它具有准多项式大小 $n^{O(\log n)}$ 和 $O(\log^2 n)$ 深度的统一电路。以前，对于具有多对数深度的此类电路的大小，仅知道指数上限。在“通信和外部信息的指数分离”中，Anat Ganor、Gillat Kol 和 Ran Raz 证明了通信任务的外部信息复杂性和通信复杂性之间的第一个差距，即指数差距。以前，这种分离仅因内部信息与通信复杂性而闻名。这个结果暗示了将通信协议压缩到它们揭示的关于输入的信息量的问题。在“用于委托计算的常量轮交互式证明”中，Omer Reingold、Guy Rothblum 和 Ron Rothblum 设计了高效的常量轮交互式证明。他们表明，对于可以在多项式时间和空间 $S$ 中评估的任何语句，都存在一个恒定轮交互协议，其中证明者具有多项式运行时间，而验证者具有大约 $n+\poly(S)$ 的运行时间。在这项工作之前，人们对恒定轮协议的力量知之甚少。这一结果是可验证的计算委托这一重大挑战的重要一步。在“Set Cover Problem 的 Single-Pass Streaming Complexity 的 Tight Bounds”中，Sepehr Assadi、Sanjeev Khanna 和 Yang Li 解决了用于逼近经典集合覆盖问题的单通道流算法的空间复杂度。为了使用单通道流算法找到 $\alpha$-approximate set cover（对于任何 $\alpha= o(\sqrt{n})$），他们表明 $\Theta(mn/\alpha)$ 空间是足够和必要的（高达 $O(\log n)$ 因子），其中 $m$ 表示集合的数量，$n$ 表示集合的大小宇宙。他们进一步研究了估计最小集合覆盖的大小（而不是寻找实际集合）的问题，并在空间复杂度中额外节省了一个因子 $\alpha$，这也是最好的。在“用于测试单调性的多项式下限”中，Aleksandrs Belovs 和 Eric Blais 展示了 $n$ 变量布尔函数的单调性自适应测试器的查询复杂度的多项式下限。在此工作之前，只有非自适应测试人员知道类似的下限，而证明自适应测试人员的类似下限一直是一项重大挑战。在“自适应数据分析的算法稳定性”中，Raef Bassily，Kobbi Nissim、Adam Smith、Thomas Steinke、Uri Stemmer 和 Jonathan Ullman 通过在差异隐私（最大 KL 稳定性）概念和自适应数据分析设计之间建立清晰、紧密的联系，在自适应数据分析领域向前迈出了坚实的一步。查询。这种联系改进了本文之前已知的一些边界，并推广到处理更多“数据分析”设置。我们感谢 STOC 2016 的作者、程序委员会成员和审稿人的辛勤工作，特别是我们感谢 SICOMP 审稿人在评估提交的论文方面所做的工作。差异隐私（最大KL稳定性）概念与自适应查询设计之间的紧密联系。这种联系改进了本文之前已知的一些边界，并推广到处理更多“数据分析”设置。我们感谢 STOC 2016 的作者、程序委员会成员和审稿人的辛勤工作，特别是我们感谢 SICOMP 审稿人在评估提交的论文方面所做的工作。差异隐私（最大KL稳定性）概念与自适应查询设计之间的紧密联系。这种联系改进了本文之前已知的一些边界，并推广到处理更多“数据分析”设置。我们感谢 STOC 2016 的作者、程序委员会成员和审稿人的辛勤工作，特别是我们感谢 SICOMP 审稿人在评估提交的论文方面所做的工作。