Proceedings of the forty-sixth annual ACM symposium on Theory of computing最新文献_第5页

Constant rank bimatrix games are PPAD-hard 固定等级双矩阵游戏是ppad难度的

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2014-02-13 DOI: 10.1145/2591796.2591835

R. Mehta

{"title":"Constant rank bimatrix games are PPAD-hard","authors":"R. Mehta","doi":"10.1145/2591796.2591835","DOIUrl":"https://doi.org/10.1145/2591796.2591835","url":null,"abstract":"The rank of a bimatrix game (A, B) is defined as rank(A + B). Computing a Nash equilibrium (NE) of a rank-0, i.e., zero-sum game is equivalent to linear programming (von Neumann'28, Dantzig'51). In 2005, Kannan and Theobald gave an FPTAS for constant rank games, and asked if there exists a polynomial time algorithm to compute an exact NE. Adsul et. al. (2011) answered this question affirmatively for rank-1 games, leaving rank-2 and beyond unresolved. In this paper we show that NE computation in games with rank ≥ 3, is PPAD-hard, settling a decade long open problem. Interestingly, this is the first instance that a problem with an FPTAS turns out to be PPAD-hard. Our reduction bypasses graphical games and game gadgets, and provides a simpler proof of PPAD-hardness for NE computation in bimatrix games. In addition, we get: • An equivalence between 2D-Linear-FIXP and PPAD, improving a result by Etessami and Yannakakis (2007) on equivalence between Linear-FIXP and PPAD. • NE computation in a bimatrix game with convex set of Nash equilibria is as hard as solving a simple stochastic game [12]. • Computing a symmetric NE of a symmetric bimatrix game with rank ≥ 6 is PPAD-hard. • Computing a 1/poly(n)-approximate fixed-point of a (Linear-FIXP) piecewise-linear function is PPAD-hard. The status of rank-2 games remains unresolved.","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129596882","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 37

A characterization of locally testable affine-invariant properties via decomposition theorems 用分解定理刻画局部可检验仿射不变性质

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2014-02-10 DOI: 10.1145/2591796.2591802

Yuichi Yoshida

引用次数: 16

Robust protocols for securely expanding randomness and distributing keys using untrusted quantum devices 使用不可信量子设备安全扩展随机性和分发密钥的鲁棒协议

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2014-02-03 DOI: 10.1145/2591796.2591843

Carl A. Miller, Yaoyun Shi

{"title":"Robust protocols for securely expanding randomness and distributing keys using untrusted quantum devices","authors":"Carl A. Miller, Yaoyun Shi","doi":"10.1145/2591796.2591843","DOIUrl":"https://doi.org/10.1145/2591796.2591843","url":null,"abstract":"Randomness is a vital resource for modern day information processing, especially for cryptography. A wide range of applications critically rely on abundant, high quality random numbers generated securely. Here we show how to expand a random seed at an exponential rate without trusting the underlying quantum devices. Our approach is secure against the most general adversaries, and has the following new features: tolerating a constant level of implementation imprecision, requiring only a unit size quantum memory per device component for the honest implementation, and allowing a large natural class of constructions. In conjunct with a recent work by Chung, Shi and Wu (QIP 2014), it leads to robust unbounded expansion using just 2 multi-part devices. It can also be adapted for distributing cryptographic keys securely. The proof begins with a known protocol and proceeds by showing that the Renyi divergence of the outputs of the protocol (for a specific bounding operator) decreases linearly as the protocol iterates. At the heart of the proof are a new uncertainty principle on quantum measurements, and a method for simulating trusted measurements with untrusted devices. A full version of this paper containing additional results developed after the conference submission is available as arXiv:1402.0489.","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130678915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 130

New algorithms and lower bounds for circuits with linear threshold gates 线性门限电路的新算法和下界

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2014-01-10 DOI: 10.1145/2591796.2591858

Ryan Williams

{"title":"New algorithms and lower bounds for circuits with linear threshold gates","authors":"Ryan Williams","doi":"10.1145/2591796.2591858","DOIUrl":"https://doi.org/10.1145/2591796.2591858","url":null,"abstract":"Let ACC o THR be the class of constant-depth circuits comprised of AND, OR, and MODm gates (for some constant m > 1), with a bottom layer of gates computing arbitrary linear threshold functions. This class of circuits can be seen as a \"midpoint\" between ACC (where we know nontrivial lower bounds) and depth-two linear threshold circuits (where nontrivial lower bounds remain open). We give an algorithm for evaluating an arbitrary symmetric function of 2no(1) ACC o THR circuits of size 2no(1), on all possible inputs, in 2n · poly(n) time. Several consequences are derived: • The number of satisfying assignments to an ACC o THR circuit of 2no(1) size is computable in 2n-ne time (where ε > 0 depends on the depth and modulus of the circuit). • NEXP does not have quasi-polynomial size ACC o THR circuits, and NEXP does not have quasi-polynomial size ACC o SYM circuits. Nontrivial size lower bounds were not known even for AND o OR o THR circuits. • Every 0-1 integer linear program with n Boolean variables and s linear constraints is solvable in 2n-Ω(n/log M)(log s)5) poly(s, n,M) time with high probability, where M upper bounds the bit complexity of the coefficients. (For example, 0-1 integer programs with weights in [--2poly(n), 2poly(n)] and poly(n) constraints can be solved in 2n-Ω(n/log6n) time.) Impagliazzo, Paturi, and Schneider [IPS13] recently gave an algorithm for Õ (n) constraints; ours is the first asymptotic improvement over exhaustive search for up to subexponentially many constraints. We also present an algorithm for evaluating depth-two linear threshold circuits (a.k.a., THR o THR) with exponential weights and 2n/24 size on all 2n input assignments, running in 2n · poly(n) time. This is evidence that non-uniform lower bounds for THR o THR are within reach.","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114422949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 86

Linear time construction of compressed text indices in compact space 紧空间中压缩文本索引的线性时间构造

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2014-01-05 DOI: 10.1145/2591796.2591885

D. Belazzougui

引用次数: 61

Optimal competitive auctions 最优竞争性拍卖

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2014-01-05 DOI: 10.1145/2591796.2591855

Ning Chen, N. Gravin, P. Lu

{"title":"Optimal competitive auctions","authors":"Ning Chen, N. Gravin, P. Lu","doi":"10.1145/2591796.2591855","DOIUrl":"https://doi.org/10.1145/2591796.2591855","url":null,"abstract":"We study the design of truthful auctions for selling identical items in unlimited supply (e.g., digital goods) to n unit demand buyers. This classic problem stands out from profit-maximizing auction design literature as it requires no probabilistic assumptions on buyers' valuations and employs the framework of competitive analysis. Our objective is to optimize the worst-case performance of an auction, measured by the ratio between a given benchmark and revenue generated by the auction. We establish a sufficient and necessary condition that characterizes competitive ratios for all monotone benchmarks. The characterization identifies the worst-case distribution of instances and reveals intrinsic relations between competitive ratios and benchmarks in the competitive analysis. With the characterization at hand, we show optimal competitive auctions for two natural benchmarks. The most well-studied benchmark F(2)(·) measures the envy-free optimal revenue where at least two buyers win. Goldberg et al. [13] showed a sequence of lower bounds on the competitive ratio for each number of buyers n. They conjectured that all these bounds are tight. We show that optimal competitive auctions match these bounds. Thus, we confirm the conjecture and settle a central open problem in the design of digital goods auctions. As one more application we examine another economically meaningful benchmark, which measures the optimal revenue across all limited supply Vickrey auctions. We identify the optimal competitive ratios to be (n/n--1)n--1 -- 1 for each number of buyers n, that is e -- 1 as n approaches infinity.","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"94 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127138285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 33

Parallel algorithms for geometric graph problems 几何图问题的并行算法

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2013-12-30 DOI: 10.1145/2591796.2591805

Alexandr Andoni, Aleksandar Nikolov, Krzysztof Onak, G. Yaroslavtsev

{"title":"Parallel algorithms for geometric graph problems","authors":"Alexandr Andoni, Aleksandar Nikolov, Krzysztof Onak, G. Yaroslavtsev","doi":"10.1145/2591796.2591805","DOIUrl":"https://doi.org/10.1145/2591796.2591805","url":null,"abstract":"We give algorithms for geometric graph problems in the modern parallel models such as MapReduce. For example, for the Minimum Spanning Tree (MST) problem over a set of points in the two-dimensional space, our algorithm computes a (1 + ε)-approximate MST. Our algorithms work in a constant number of rounds of communication, while using total space and communication proportional to the size of the data (linear space and near linear time algorithms). In contrast, for general graphs, achieving the same result for MST (or even connectivity) remains a challenging open problem [9], despite drawing significant attention in recent years. We develop a general algorithmic framework that, besides MST, also applies to Earth-Mover Distance (EMD) and the transportation cost problem. Our algorithmic framework has implications beyond the MapReduce model. For example it yields a new algorithm for computing EMD cost in the plane in near-linear time, n1+oε(1). We note that while recently [33] have developed a near-linear time algorithm for (1 + ε)-approximating EMD, our algorithm is fundamentally different, and, for example, also solves the transportation (cost) problem, raised as an open question in [33]. Furthermore, our algorithm immediately gives a (1+ ε)-approximation algorithm with nδ space in the streaming-with-sorting model with 1/δO(1) passes. As such, it is tempting to conjecture that the parallel models may also constitute a concrete playground in the quest for efficient algorithms for EMD (and other similar problems) in the vanilla streaming model, a well-known open problem.","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122914982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 169

Faster all-pairs shortest paths via circuit complexity 更快的全对最短路径通过电路复杂度

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2013-12-23 DOI: 10.1145/2591796.2591811

Ryan Williams

{"title":"Faster all-pairs shortest paths via circuit complexity","authors":"Ryan Williams","doi":"10.1145/2591796.2591811","DOIUrl":"https://doi.org/10.1145/2591796.2591811","url":null,"abstract":"We present a new randomized method for computing the min-plus product (a.k.a., tropical product) of two n × n matrices, yielding a faster algorithm for solving the all-pairs shortest path problem (APSP) in dense n-node directed graphs with arbitrary edge weights. On the real RAM, where additions and comparisons of reals are unit cost (but all other operations have typical logarithmic cost), the algorithm runs in time [EQUATION] and is correct with high probability. On the word RAM, the algorithm runs in [EQUATION] + n2+o(1) logM time for edge weights in ([0,M]∩Z)∪{∞}. Prior algorithms took either O(n3/logc n) time for various c ≤ 2, or O(Mαnβ) time for various α > 0 and β > 2. The new algorithm applies a tool from circuit complexity, namely the Razborov-Smolensky polynomials for approximately representing AC0[p] circuits, to efficiently reduce a matrix product over the (min, +) algebra to a relatively small number of rectangular matrix products over F2, each of which are computable using a particularly efficient method due to Coppersmith. We also give a deterministic version of the algorithm running in n[EQUATION] time for some δ > 0, which utilizes the Yao-Beigel-Tarui translation of AC0[m] circuits into \"nice\" depth-two circuits.","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"211 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116227034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 257

Rounding sum-of-squares relaxations 四舍五入平方和松弛

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2013-12-23 DOI: 10.1145/2591796.2591886

B. Barak, Jonathan A. Kelner, David Steurer

引用次数: 115

Optimal error rates for interactive coding I: adaptivity and other settings 交互编码的最佳错误率I:适应性和其他设置

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2013-12-06 DOI: 10.1145/2591796.2591872

M. Ghaffari, Bernhard Haeupler, M. Sudan

{"title":"Optimal error rates for interactive coding I: adaptivity and other settings","authors":"M. Ghaffari, Bernhard Haeupler, M. Sudan","doi":"10.1145/2591796.2591872","DOIUrl":"https://doi.org/10.1145/2591796.2591872","url":null,"abstract":"We consider the task of interactive communication in the presence of adversarial errors and present tight bounds on the tolerable error-rates in a number of different settings. Most significantly, we explore adaptive interactive communication where the communicating parties decide who should speak next based on the history of the interaction. In particular, this decision can depend on estimates of the amount of errors that have occurred so far. Braverman and Rao [STOC'11] show that non-adaptively one can code for any constant error rate below 1/4 but not more. They asked whether this bound could be improved using adaptivity. We answer this open question in the affirmative (with a slightly different collection of resources): Our adaptive coding scheme tolerates any error rate below 2/7 and we show that tolerating a higher error rate is impossible. We also show that in the setting of Franklin et al. [CRYPTO'13], where parties share randomness not known to the adversary, adaptivity increases the tolerable error rate from 1/2 to 2/3. For list-decodable interactive communications, where each party outputs a constant size list of possible outcomes, the tight tolerable error rate is 1/2. Our negative results hold even if the communication and computation are unbounded, whereas for our positive results communication and computations are polynomially bounded. Most prior work considered coding schemes with linear communication bounds, while allowing unbounded computations. We argue that studying tolerable error rates in this relaxed context helps to identify a setting's intrinsic optimal error rate. We set forward a strong working hypothesis which stipulates that for any setting the maximum tolerable error rate is independent of many computational and communication complexity measures. We believe this hypothesis to be a powerful guideline for the design of simple, natural, and efficient coding schemes and for understanding the (im)possibilities of coding for interactive communications.","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132292865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 74