Proceedings of the forty-sixth annual ACM symposium on Theory of computing最新文献_第3页

Hitting sets for multilinear read-once algebraic branching programs, in any order 任意顺序的多线性一次读代数分支程序的命中集

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2014-05-31 DOI: 10.1145/2591796.2591816

Michael A. Forbes, Ramprasad Saptharishi, Amir Shpilka

{"title":"Hitting sets for multilinear read-once algebraic branching programs, in any order","authors":"Michael A. Forbes, Ramprasad Saptharishi, Amir Shpilka","doi":"10.1145/2591796.2591816","DOIUrl":"https://doi.org/10.1145/2591796.2591816","url":null,"abstract":"We give deterministic black-box polynomial identity testing algorithms for multilinear read-once oblivious algebraic branching programs (ROABPs), in nO(log2 n) time. Further, our algorithm is oblivious to the order of the variables. This is the first sub-exponential time algorithm for this model. Furthermore, our result has no known analogue in the model of read-once oblivious boolean branching programs with unknown order. We obtain our results by recasting, and improving upon, the ideas of Agrawal, Saha and Saxena [ASS13]. We phrase the ideas in terms of rank condensers and Wronskians, and show that our results improve upon the classical multivariate Wronskian, which may be of independent interest. In addition, we give the first nO(lg lg n) black-box polynomial identity testing algorithm for the so called model of diagonal circuits. This result improves upon the nΘ(lg n)-time algorithms given by Agrawal, Saha and Saxena [ASS13], and Forbes and Shpilka [FS13b] for this class. More generally, our result holds for any model computing polynomials whose partial derivatives (of all orders) span a low dimensional linear space.","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":"2014-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130327800","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: 58

Sublinear-time decremental algorithms for single-source reachability and shortest paths on directed graphs 有向图上单源可达性和最短路径的次线性时间递减算法

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2014-05-31 DOI: 10.1145/2591796.2591869

M. Henzinger, Sebastian Krinninger, Danupon Nanongkai

{"title":"Sublinear-time decremental algorithms for single-source reachability and shortest paths on directed graphs","authors":"M. Henzinger, Sebastian Krinninger, Danupon Nanongkai","doi":"10.1145/2591796.2591869","DOIUrl":"https://doi.org/10.1145/2591796.2591869","url":null,"abstract":"We consider dynamic algorithms for maintaining Single-Source Reachability (SSR) and approximate Single-Source Shortest Paths (SSSP) on n-node m-edge directed graphs under edge deletions (decremental algorithms). The previous fastest algorithm for SSR and SSSP goes back three decades to Even and Shiloach (JACM 1981); it has O(1) query time and O(mn) total update time (i.e., linear amortized update time if all edges are deleted). This algorithm serves as a building block for several other dynamic algorithms. The question whether its total update time can be improved is a major, long standing, open problem. In this paper, we answer this question affirmatively. We obtain a randomized algorithm which, in a simplified form, achieves an Õ(mn0.984) expected total update time for SSR and (1 + ε)-approximate SSSP, where Õ(·) hides poly log n. We also extend our algorithm to achieve roughly the same running time for Strongly Connected Components (SCC), improving the algorithm of Roditty and Zwick (FOCS 2002), and an algorithm that improves the Õ (mn log W)-time algorithm of Bernstein (STOC 2013) for approximating SSSP on weighted directed graphs, where the edge weights are integers from 1 to W. All our algorithms have constant query time in the worst case.","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"618 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131508065","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: 63

Lower bounds for depth 4 formulas computing iterated matrix multiplication 深度4公式计算迭代矩阵乘法的下界

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2014-05-31 DOI: 10.1145/2591796.2591824

Hervé Fournier, N. Limaye, Guillaume Malod, S. Srinivasan

引用次数: 85

Turnstile streaming algorithms might as well be linear sketches 旋转门流算法也可以是线性草图

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2014-05-31 DOI: 10.1145/2591796.2591812

Yi Li, Huy L. Nguyen, David P. Woodruff

{"title":"Turnstile streaming algorithms might as well be linear sketches","authors":"Yi Li, Huy L. Nguyen, David P. Woodruff","doi":"10.1145/2591796.2591812","DOIUrl":"https://doi.org/10.1145/2591796.2591812","url":null,"abstract":"In the turnstile model of data streams, an underlying vector x ∈ {--m,--m+1,..., m--1,m}n is presented as a long sequence of positive and negative integer updates to its coordinates. A randomized algorithm seeks to approximate a function f(x) with constant probability while only making a single pass over this sequence of updates and using a small amount of space. All known algorithms in this model are linear sketches: they sample a matrix A from a distribution on integer matrices in the preprocessing phase, and maintain the linear sketch A·x while processing the stream. At the end of the stream, they output an arbitrary function of A · x. One cannot help but ask: are linear sketches universal? In this work we answer this question by showing that any 1-pass constant probability streaming algorithm for approximating an arbitrary function f of x in the turnstile model can also be implemented by sampling a matrix A from the uniform distribution on O(n logm) integer matrices, with entries of magnitude poly(n), and maintaining the linear sketch Ax. Furthermore, the logarithm of the number of possible states of Ax, as x ranges over {--m,--m + 1,..., m}n, plus the amount of randomness needed to store A, is at most a logarithmic factor larger than the space required of the space-optimal algorithm. Our result shows that to prove space lower bounds for 1-pass streaming algorithms, it suffices to prove lower bounds in the simultaneous model of communication complexity, rather than the stronger 1-way model. Moreover, the fact that we can assume we have a linear sketch with polynomially-bounded entries further simplifies existing lower bounds, e.g., for frequency moments we present a simpler proof of the Ω(n1-2/k) bit complexity lower bound without using communication complexity.","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123866335","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: 98

Black-box non-black-box zero knowledge 黑箱非黑箱零知识

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2014-05-31 DOI: 10.1145/2591796.2591879

Vipul Goyal, R. Ostrovsky, Alessandra Scafuro, Ivan Visconti

{"title":"Black-box non-black-box zero knowledge","authors":"Vipul Goyal, R. Ostrovsky, Alessandra Scafuro, Ivan Visconti","doi":"10.1145/2591796.2591879","DOIUrl":"https://doi.org/10.1145/2591796.2591879","url":null,"abstract":"Motivated by theoretical and practical interest, the challenging task of designing cryptographic protocols having only black-box access to primitives has generated various breakthroughs in the last decade. Despite such positive results, even though nowadays we know black-box constructions for secure two-party and multi-party computation even in constant rounds, there still are in Cryptography several constructions that critically require non-black-box use of primitives in order to securely realize some fundamental tasks. As such, the study of the gap between black-box and nonblack-box constructions still includes major open questions. In this work we make progress towards filling the above gap. We consider the case of black-box constructions for computations requiring that even the size of the input of a player remains hidden. We show how to commit to a string of arbitrary size and to prove statements over the bits of the string. Both the commitment and the proof are succinct, hide the input size and use standard primitives in a blackbox way. We achieve such a result by giving a black-box construction of an extendable Merkle tree that relies on a novel use of the \"MPC in the head\" paradigm of Ishai et al. [STOC 2007]. We show the power of our new techniques by giving the first black-box constant-round public-coin zero knowledge argument for NP. To achieve this result we use the nonblack-box simulation technique introduced by Barak [FOCS 2001], the PCP of Proximity introduced by Ben-Sasson et al. [STOC 2004], together with a black-box public-coin witness indistinguishable universal argument that we construct along the way.","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":"2014-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123738641","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: 25

On derandomizing algorithms that err extremely rarely 关于极少出错的非随机化算法

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2014-05-31 DOI: 10.1145/2591796.2591808

Oded Goldreich, A. Wigderson

{"title":"On derandomizing algorithms that err extremely rarely","authors":"Oded Goldreich, A. Wigderson","doi":"10.1145/2591796.2591808","DOIUrl":"https://doi.org/10.1145/2591796.2591808","url":null,"abstract":"Does derandomization of probabilistic algorithms become easier when the number of \"bad\" random inputs is extremely small? In relation to the above question, we put forward the following quantified derandomization challenge: For a class of circuits C (e.g., P/poly or AC0, AC0[2]) and a bounding function B: N → N (e.g., B(n) = nlog n or B(n) = exp(n0.99))), given an n-input circuit C from C that evaluates to 1 on all but at most B(n) of its inputs, find (in deterministic polynomial-time) an input x such that C(x) = 1. Indeed, the standard derandomization challenge for the class C corresponds to the case of B(n) = 2n/2 (or to B(n) = 2n/3 for the two-sided version case). Our main results regarding the new quantified challenge are: 1. Solving the quantified derandomization challenge for the class AC0 and every sub-exponential bounding function (e.g., B(n) = exp(n0.999)). 2. Showing that solving the quantified derandomization challenge for the class AC0[2] and any sub-exponential bounding function (e.g., B(n) = exp(n0.001)), implies solving the standard derandomization challenge for the class AC0[2] (i.e., for B(n) = 2n/2). Analogous results are obtained also for stronger (Black-box) forms of efficient derandomization like hitting-set generators. We also obtain results for other classes of computational devices including log-space algorithms and Arithmetic circuits. For the latter we present a deterministic polynomial-time hitting set generator for the class of n-variate polynomials of degree d over GF(2) that evaluate to 0 on at most an O(2-d) fraction of their inputs. In general, the quantified derandomization problem raises a variety of seemingly unexplored questions about many randomized complexity classes, and may offer a tractable approach to unconditional derandomization for some of them.","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122036439","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: 27

Approximation algorithms for bipartite matching with metric and geometric costs 具有度量和几何代价的二部匹配的近似算法

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2014-05-31 DOI: 10.1145/2591796.2591844

P. Agarwal, R. Sharathkumar

{"title":"Approximation algorithms for bipartite matching with metric and geometric costs","authors":"P. Agarwal, R. Sharathkumar","doi":"10.1145/2591796.2591844","DOIUrl":"https://doi.org/10.1145/2591796.2591844","url":null,"abstract":"Let G = G(A∪B,A×B), with |A| = |B| = n, be a weighted bipartite graph, and let d(·,·) be the cost function on the edges. Let w(M) denote the weight of a matching in G, and M* a minimum-cost perfect matching in G. We call a perfect matching M c-approximate, for c ≥ 1, if w(M) ≤ c · w(M*). We present three approximation algorithms for computing minimum-cost perfect matchings in G. First, we consider the case when d(·,·) is a metric. For any δ > 0, we present an algorithm that, in O(n2+δ log n log2(1/δ)) time, computes a O(1/δα)-approximate matching of G, where α = log3 2 ≈ 0.631. Next, we assume the existence of a dynamic data structure for answering approximate nearest neighbor (ANN) queries under d(··). Given two parameters ε, &delta ∈ (0, 1), we present an algorithm that, in O(ε---2n1+δτ (n, ε) log2(n/ε) log(1/δ)) time, computes a O(1/δα)-approximate matching of G, where α = 1 + log2(1 + ε) and τ (n; ε) is the query and update time of an (ε/2)-ANN data structure. Finally, we present an algorithm that works even if d(·,·) is not a metric but admits an ANN data structure for d(·,·). In particular, we present an algorithm that computes, in O(ε---1n3/2τ (n, ε) log4(n/ε) log Δ) time, a (1 + ε)-approximate matching of A and B; here Δ is the ratio of the largest to the smallest-cost edge in G, and τ (n, ε) is the query and update time of an (ε/c)-ANN data structure for some constant c > 1. We show that our results lead to faster matching algorithms for many geometric settings.","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117156422","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: 45

Infinite randomness expansion with a constant number of devices 无限随机扩展与恒定数量的设备

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2014-05-31 DOI: 10.1145/2591796.2591873

Matthew Coudron, H. Yuen

{"title":"Infinite randomness expansion with a constant number of devices","authors":"Matthew Coudron, H. Yuen","doi":"10.1145/2591796.2591873","DOIUrl":"https://doi.org/10.1145/2591796.2591873","url":null,"abstract":"We present a device-independent randomness expansion protocol, involving only a constant number of non-signaling quantum devices, that achieves infinite expansion: starting with m bits of uniform private randomness, the protocol can produce an unbounded amount of certified randomness that is exp(--Ω(m1/3))-close to uniform and secure against a quantum adversary. The only parameters which depend on the size of the input are the soundness of the protocol and the security of the output (both are inverse exponential in m). This settles a long-standing open problem in the area of randomness expansion and device-independence. The analysis of our protocols involves overcoming fundamental challenges in the study of adaptive device-independent protocols. Our primary technical contribution is the design and analysis of device-independent protocols which are Input Secure; that is, their output is guaranteed to be secure against a quantum eavesdropper, even if the input randomness was generated by that same eavesdropper! The notion of Input Security may be of independent interest to other areas such as device-independent quantum key distribution.","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126396693","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: 52

Analyze gauss: optimal bounds for privacy-preserving principal component analysis 分析高斯:隐私保护主成分分析的最优界

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2014-05-31 DOI: 10.1145/2591796.2591883

C. Dwork, Kunal Talwar, Abhradeep Thakurta, Li Zhang

{"title":"Analyze gauss: optimal bounds for privacy-preserving principal component analysis","authors":"C. Dwork, Kunal Talwar, Abhradeep Thakurta, Li Zhang","doi":"10.1145/2591796.2591883","DOIUrl":"https://doi.org/10.1145/2591796.2591883","url":null,"abstract":"We consider the problem of privately releasing a low dimensional approximation to a set of data records, represented as a matrix A in which each row corresponds to an individual and each column to an attribute. Our goal is to compute a subspace that captures the covariance of A as much as possible, classically known as principal component analysis (PCA). We assume that each row of A has ℓ2 norm bounded by one, and the privacy guarantee is defined with respect to addition or removal of any single row. We show that the well-known, but misnamed, randomized response algorithm, with properly tuned parameters, provides nearly optimal additive quality gap compared to the best possible singular subspace of A. We further show that when ATA has a large eigenvalue gap -- a reason often cited for PCA -- the quality improves significantly. Optimality (up to logarithmic factors) is proved using techniques inspired by the recent work of Bun, Ullman, and Vadhan on applying Tardos's fingerprinting codes to the construction of hard instances for private mechanisms for 1-way marginal queries. Along the way we define a list culling game which may be of independent interest. By combining the randomized response mechanism with the well-known following the perturbed leader algorithm of Kalai and Vempala we obtain a private online algorithm with nearly optimal regret. The regret of our algorithm even outperforms all the previously known online non-private algorithms of this type. We achieve this better bound by, satisfyingly, borrowing insights and tools from differential privacy!","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130993937","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: 249

Constant factor approximation for balanced cut in the PIE model PIE模型中平衡切口的常因子近似

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2014-05-31 DOI: 10.1145/2591796.2591841

K. Makarychev, Yury Makarychev, Aravindan Vijayaraghavan

引用次数: 27