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 been revised and extended by the authors and subjected to the standard thorough reviewing process of SICOMP. The program committee consisted of Dimitris Achlioptas (University of California, Santa Cruz), Dorit Aharonov (Hebrew University), Susanne Albers (Technical University Munich), Eric Allender (Rutgers University), Sayan Bhattacharya (University of Warwick), Richard Cole (New York University), Vitaly Feldman (Google Research), Uriel Feige (Weizmann Institute), Sanjam Garg (University of California, Berkeley), Ashish Goel (Stanford University), Parikshit Gopalan (VMware), Monika Henzinger, chair (University of Vienna), Giuseppe Italiano (Luiss University), Robert Kleinberg (Cornell University), Claire Matthieu (École Normale Supérieure, CNRS), Ankur Moitra (Massachusetts Institute of Technology), Danupon Nanongkai (KTH Royal Institute of Technology, Stockholm), Michał Pilipczuk (University of Warsaw), Krzysztof Pietrzak (Institute of Science and Technology, Austria), Aaron Sidford (Stanford University), Christian Sohler (Universität zu Köln), Prasad Tetali (Georgia Institute of Technology), Kunal Talwar (Apple), Luca Trevisan (Bocconi University), Thomas Vidick (California Institute of Technology), Emo Welzl (ETH Zurich), Philipp Woelfel (University of Calgary), David Woodruff (Carnegie Mellon University), and Mary Wootters (Stanford University). They selected 112 papers out of 416 submissions. We briefly describe the papers that appear here. In “Round Compression for Parallel Matching Algorithms,” Artur Czumaj, Jakub Ła̧cki, Aleksander Ma̧dry, Slobodan Mitrović, Krzysztof Onak, and Piotr Sankowski break the $O(\log n)$ round complexity bound for 2-approximating the maximum matching in near-linear memory regime of the massively parallel computation model. In “Smooth Heaps and a Dual View of Self-Adjusting Data Structures,” László Kozma and Thatchaphol Saranurak show a new correspondence between self-adjusting binary search trees (BSTs) and heaps. Using this connection they are able to transfer known lower bounds on BSTs to a general model of heaps as well as obtain a new, simple, and efficient heap algorithm called the “smooth heap.” In “Collusion Resistant Traitor Tracing from Learning with Errors," Rishab Goyal, Venkata Koppula, and Brent Waters introduce a new approach to the traitor tracing problem. Informally, in traitor tracing one aims to devise an encryption scheme such that decryption can be performed using $n$ different private keys and such that moreover any decryption can be “traced back" to the key(s) that was or were used for it. In this paper the authors obtain the first scheme with ciphertext size that grows polynomially in $\log(n)$ and the security parameter $\lambda$ and whose security is based on the learning with errors assumption. In “Pseudorandom Pseudo-distributions with Near-Optimal Error for Read-Once Branching Programs,” Mark Braverman, Gil Cohen, and Sumegha Garg construct a hitting set for unrestricted read-once branching programs with seed length $O(\log^2n + \log(1/\varepsilon))$. This is the first improvement since Nisan's pseudorandom generator with seed length $O(\log^2n + \log n \log(1/\varepsilon)$. In “Circuit Lower Bounds for Nondeterministic Quasi-Polytime from a New Easy Witness Lemma,” Cody Murray and Ryan Williams show that if every problem in NP has polynomial-size circuits for a fixed polynomial, then every problem in NP also has a fixed polynomial-size witness. A specific consequence of this result is that for every fixed $k$, NQP does not have $n^{\log^k n}$-size ACC$\circ$THR circuits. In “Crossing the Logarithmic Barrier for Dynamic Boolean Data Structure Lower Bounds,” Kasper Green Larsen, Omri Weinstein, and Huacheng Yu prove the first superlogarithmic lower bounds on the cell probe complexity of dynamic Boolean data structure problems, a long-standing milestone in data structure lower bounds. In “Shadow Tomography of Quantum States,” Scott Aaronson asks: Given an unknown $D$-dimensional quantum mixed state $\rho$ and two-outcome measurements $E_1, \ldots, E_M$, how many copies of $\rho$ are needed to estimate the probability that $E_i$ accepts $\rho$ to within additive error $\varepsilon$, for each of the $M$ measurements? He shows that $O(\varepsilon^{-4} \log^4 M \log D)$ copies of $\rho$ suffice, implying, for example, that we can learn the behavior of an arbitrary $n$-qubit state, on all accepting/rejecting circuits of some fixed polynomial size, by measuring only $n^{O(1)}$ copies of the state. In “Inapproximability of the Independent Set Polynomial in the Complex Plane,” Ivona Bezáková, Andreas Galanis, Leslie Ann Goldberg, and Daniel Štefankovič study the complexity of approximating the independent set polynomial of a graph with maximum degree $\Delta$ when the activity $\lambda$ is a complex number. They prove that outside a cardioid-shaped region in the complex plane identified by Peters and Regts, wherein the occupation ratios of $\Delta$-regular trees converge, approximation is $\#$P-hard (unless $\lambda$ is a positive real number, in which case it is NP-hard). In “A Friendly Smoothed Analysis of the Simplex Method,” Daniel Dadush and Sophie Huiberts consider linear programs with $d$ variables and $n$ constraints, smoothed by the addition of Gaussian noise with variance $\sigma^2$. They provide an improved and greatly simplified analysis of shadow simplex methods by combining an improved shadow bound with improvements on algorithmic techniques of Vershynin and show that in expectation $O(d^2 \sqrt{\log n} \, \sigma^{-2} + d^3 \log^{3/2}n)$ pivots suffice. In “Nearly Work-Efficient Parallel Algorithm for Digraph Reachability,” Jeremy T. Fineman presents a randomized parallel algorithm for digraph reachability and related problems with expected work $\tilde{O}(m)$ and span $\tilde{O}(n^{2/3})$. This is the first parallel algorithm having both nearly linear work and strongly sublinear span.

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第五十届ACM计算理论年度学术研讨会特别部分（STOC 2018）

SIAM计算杂志，第49卷，第5期，第STOC18-i-STOC18-ii页，2020年1月。
本期SICOMP包含6月25日至29日在加利福尼亚州洛杉矶举行的第50届ACM计算理论年度研讨会（也称为STOC 2018）中精选的10篇论文。选择这里的论文代表STOC计划的卓越和广泛。这些文件已由作者进行了修订和扩展，并经过了SICOMP的标准彻底审查。该计划委员会由Dimitris Achlioptas（加利福尼亚大学，圣克鲁斯大学），Dorit Aharonov（希伯来大学），Susanne Albers（慕尼黑工业大学），Eric Allender（罗格斯大学），Sayan Bhattacharya（沃里克大学），Richard Cole（新成立）组成约克大学），维塔利·费尔德曼（Vitaly Feldman）（谷歌研究），乌里尔·费格（Ureel Feige）（魏茨曼研究所），桑杰姆·加格（Sanjam Garg）（加利福尼亚大学伯克利分校）他们从416篇论文中选择了112篇论文。我们简要描述这里出现的论文。在“并行匹配算法的圆形压缩”中，Artur Czumaj，JakubŁa̧cki，AleksanderMa̧dry，SlobodanMitrović，Krzysztof Onak和Piotr Sankowski打破了$ O（\ log n）$的复杂度，使2在附近近似最大匹配。并行计算模型的线性存储机制。LászlóKozma和Thatchaphol Saranurak在“平滑堆和自调整数据结构的双重视图”中，展示了自调整二进制搜索树（BST）与堆之间的新对应关系。使用此连接，他们能够将BST上的已知下限转移到一般的堆模型中，并获得称为“平滑堆”的新的，简单而有效的堆算法。Rishab Goyal，Venkata Koppula和Brent Waters在“从错误学习中获得的防止共谋叛国者追踪”中，介绍了一种解决叛徒追踪问题的新方法。非正式地，在叛徒追踪中，一个目的是设计一种加密方案，以便可以执行解密。使用$ n $个不同的私钥，因此，任何解密都可以“追溯到”曾经或曾经使用过的密钥。在本文中，作者获得了第一种方案，其密文大小在$ \ log（n）$和安全参数$ \ lambda $中呈多项式增长，并且其安全性基于对错误假设的学习。在“一次读取分支程序的具有接近最佳错误的伪随机伪分布”中，Mark Braverman，Gil Cohen和 Sumegha Garg和Sumegha Garg为种子长度为$ O（\ log ^ 2n + \ log（1 / \ varepsilon））$的不受限制的一次读取分支程序构造了一个命中集。这是自Nisan伪随机数生成器以来的第一个改进，其种子长度为$ O（\ log ^ 2n + \ log n \ log（1 / \ varepsilon）$。在“通过新的简单见证引理进行不确定的准时限的电路下界”中， ” Cody Murray和Ryan Williams表明，如果NP中的每个问题都有一个固定多项式的多项式大小的电路，那么NP中的每个问题也都有一个固定的多项式大小的见证人。这个结果的特定结果是，每固定一个$ k $，NQP没有$ n ^ {\ log ^ kn} $大小的ACC $ \ circ $ THR电路。在“跨越动态布尔数据结构下界的对数障碍”中，Kasper Green Larsen，Omri Weinstein，Yuhua和Yucheng证明了动态布尔数据结构问题的单元探针复杂度的第一个超对数下界，这是数据结构下界的一个长期里程碑。在《量子态的阴影层析成像》中，斯科特·亚伦森问：给定未知的$ D $维量子混合态$ \ rho $和两次测量结果$ E_1，\ ldots，E_M $，$ \ rho $多少个副本对于每个$ M $测量值，需要估计$ E_i $接受$ \ rho $到加性误差$ \ varepsilon $内的概率吗？他表明$ O（\ varepsilon ^ {-4} \ log ^ 4 M \ log D）$的$ \ rho $副本就足够了，例如，这意味着我们可以学习任意$ n $ -qubit的行为。通过仅测量该状态的$ n ^ {O（1）} $个副本，在某个固定多项式大小的所有接受/拒绝电路上确定状态。在“复杂平面中独立集合多项式的不可逼近”中，伊沃娜·贝扎科夫（IvonaBezáková），安德烈亚斯·加拉尼斯（Andreas Galanis），莱斯利·安·戈德伯格（Leslie Ann Goldberg）和丹尼尔·斯特凡科维奇（DanielŠtefankovič）研究了当活动$ \ lambda $是一个复数。他们证明了在由Peters and Regts识别的复杂平面中的心形形状区域之外，其中$ \ Delta $-常规树的占用比率收敛，近似值为$ \＃$ P-hard（除非$ \ lambda $是正实数，在这种情况下为NP-hard）。在“单纯形方法的友好平滑分析”中，Daniel Dadush和Sophie Huiberts考虑了具有$ d $变量和$ n $约束的线性程序，通过添加具有方差$ \ sigma ^ 2 $的高斯噪声进行平滑。他们通过结合改进的阴影边界和Vershynin算法技术的改进，提供了一种改进的阴影简化方法，并且大大简化了分析，并显示出期望$ O（d ^ 2 \ sqrt {\ log n} \，\ sigma ^ {- 2} + d ^ 3 \ log ^ {3/2} n）$枢轴就足够了。Jeremy T. Fineman在“几乎有效率的有向图可达性并行算法”中，提出了一种有向图可达性和预期工作$ \ tilde {O}（m）$和跨度$ \ tilde {O}（ n ^ {2/3}）$。这是第一个并行算法，具有几乎线性工作和强次线性范围。Jeremy T. Fineman在“几乎有效率的有向图可达性并行算法”中，提出了一种有向图可达性和预期工作$ \ tilde {O}（m）$和跨度$ \ tilde {O}（ n ^ {2/3}）$。这是第一个同时具有近似线性工作和强次线性跨度的并行算法。Jeremy T. Fineman在“几乎有效率的有向图可达性并行算法”中，提出了一种有向图可达性及预期工作$ \ tilde {O}（m）$和跨度$ \ tilde {O}（ n ^ {2/3}）$。这是第一个同时具有近似线性工作和强次线性跨度的并行算法。