Proceedings of the forty-seventh annual ACM symposium on Theory of Computing最新文献_第4页

From Independence to Expansion and Back Again 从独立到扩张再回来

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 2015-06-11 DOI: 10.1145/2746539.2746620

Tobias Christiani, R. Pagh, M. Thorup

引用次数: 17

Polynomially Low Error PCPs with polyloglog n Queries via Modular Composition 基于模组合的多对数n查询多项式低误差pcp

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 2015-05-23 DOI: 10.1145/2746539.2746630

Irit Dinur, P. Harsha, Guy Kindler

{"title":"Polynomially Low Error PCPs with polyloglog n Queries via Modular Composition","authors":"Irit Dinur, P. Harsha, Guy Kindler","doi":"10.1145/2746539.2746630","DOIUrl":"https://doi.org/10.1145/2746539.2746630","url":null,"abstract":"We show that every language in NP has a PCP verifier that tosses O(log n) random coins, has perfect completeness, and a soundness error of at most 1/poly(n), while making O(poly log log n) queries into a proof over an alphabet of size at most n1/poly log log n. Previous constructions that obtain 1/poly(n) soundness error used either poly log n queries or an exponential alphabet, i.e. of size 2nc for some c> 0. Our result is an exponential improvement in both parameters simultaneously. Our result can be phrased as polynomial-gap hardness for approximate CSPs with arity poly log log n and alphabet size n1/poly log n. The ultimate goal, in this direction, would be to prove polynomial hardness for CSPs with constant arity and polynomial alphabet size (aka the sliding scale conjecture for inverse polynomial soundness error). Our construction is based on a modular generalization of previous PCP constructions in this parameter regime, which involves a composition theorem that uses an extra 'consistency' query but maintains the inverse polynomial relation between the soundness error and the alphabet size. Our main technical/conceptual contribution is a new notion of soundness, which we refer to as distributional soundness, that replaces the previous notion of \"list decoding soundness\", and allows us to invoke composition a super-constant number of times without incurring a blow-up in the soundness error.","PeriodicalId":20566,"journal":{"name":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2015-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79688281","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: 15

A Polynomial-time Bicriteria Approximation Scheme for Planar Bisection 平面剖分的多项式时间双准则逼近格式

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 2015-04-29 DOI: 10.1145/2746539.2746564

K. Fox, P. Klein, S. Mozes

引用次数: 7

On the Lovász Theta function for Independent Sets in Sparse Graphs 稀疏图中独立集的Lovász θ函数

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 2015-04-18 DOI: 10.1145/2746539.2746607

N. Bansal, Anupam Gupta, Guru Guruganesh

引用次数: 28

Local, Private, Efficient Protocols for Succinct Histograms 简洁直方图的本地、私有、高效协议

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 2015-04-17 DOI: 10.1145/2746539.2746632

Raef Bassily, Adam D. Smith

{"title":"Local, Private, Efficient Protocols for Succinct Histograms","authors":"Raef Bassily, Adam D. Smith","doi":"10.1145/2746539.2746632","DOIUrl":"https://doi.org/10.1145/2746539.2746632","url":null,"abstract":"We give efficient protocols and matching accuracy lower bounds for frequency estimation in the local model for differential privacy. In this model, individual users randomize their data themselves, sending differentially private reports to an untrusted server that aggregates them. We study protocols that produce a succinct histogram representation of the data. A succinct histogram is a list of the most frequent items in the data (often called \"heavy hitters\") along with estimates of their frequencies; the frequency of all other items is implicitly estimated as 0. If there are n users whose items come from a universe of size d, our protocols run in time polynomial in n and log(d). With high probability, they estimate the accuracy of every item up to error O(√{log(d)/(ε2n)}). Moreover, we show that this much error is necessary, regardless of computational efficiency, and even for the simple setting where only one item appears with significant frequency in the data set. Previous protocols (Mishra and Sandler, 2006; Hsu, Khanna and Roth, 2012) for this task either ran in time Ω(d) or had much worse error (about √[6]{log(d)/(ε2n)}), and the only known lower bound on error was Ω(1/√{n}). We also adapt a result of McGregor et al (2010) to the local setting. In a model with public coins, we show that each user need only send 1 bit to the server. For all known local protocols (including ours), the transformation preserves computational efficiency.","PeriodicalId":20566,"journal":{"name":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2015-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91087294","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: 373

Testing Cluster Structure of Graphs 测试图的聚类结构

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 2015-04-13 DOI: 10.1145/2746539.2746618

A. Czumaj, Pan Peng, C. Sohler

引用次数: 29

Learning Arbitrary Statistical Mixtures of Discrete Distributions 学习离散分布的任意统计混合

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 2015-04-09 DOI: 10.1145/2746539.2746584

Jian Li, Y. Rabani, L. Schulman, Chaitanya Swamy

引用次数: 19

Byzantine Agreement with Optimal Early Stopping, Optimal Resilience and Polynomial Complexity 具有最优提前停止、最优弹性和多项式复杂度的拜占庭协议

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 2015-04-09 DOI: 10.1145/2746539.2746581

Ittai Abraham, D. Dolev

引用次数: 22

Space- and Time-Efficient Algorithm for Maintaining Dense Subgraphs on One-Pass Dynamic Streams 一遍动态流上保持密集子图的空间和时间效率算法

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 2015-04-09 DOI: 10.1145/2746539.2746592

Sayan Bhattacharya, M. Henzinger, Danupon Nanongkai, Charalampos E. Tsourakakis

{"title":"Space- and Time-Efficient Algorithm for Maintaining Dense Subgraphs on One-Pass Dynamic Streams","authors":"Sayan Bhattacharya, M. Henzinger, Danupon Nanongkai, Charalampos E. Tsourakakis","doi":"10.1145/2746539.2746592","DOIUrl":"https://doi.org/10.1145/2746539.2746592","url":null,"abstract":"While in many graph mining applications it is crucial to handle a stream of updates efficiently in terms of both time and space, not much was known about achieving such type of algorithm. In this paper we study this issue for a problem which lies at the core of many graph mining applications called densest subgraph problem. We develop an algorithm that achieves time- and space-efficiency for this problem simultaneously. It is one of the first of its kind for graph problems to the best of our knowledge. Given an input graph, the densest subgraph is the subgraph that maximizes the ratio between the number of edges and the number of nodes. For any ε>0, our algorithm can, with high probability, maintain a (4+ε)-approximate solution under edge insertions and deletions using ~O(n) space and ~O(1) amortized time per update; here, $n$ is the number of nodes in the graph and ~O hides the O(polylog_{1+ε} n) term. The approximation ratio can be improved to (2+ε) with more time. It can be extended to a (2+ε)-approximation sublinear-time algorithm and a distributed-streaming algorithm. Our algorithm is the first streaming algorithm that can maintain the densest subgraph in one pass. Prior to this, no algorithm could do so even in the special case of an incremental stream and even when there is no time restriction. The previously best algorithm in this setting required O(log n) passes [BahmaniKV12]. The space required by our algorithm is tight up to a polylogarithmic factor.","PeriodicalId":20566,"journal":{"name":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2015-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73985031","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: 127

Learning Mixtures of Gaussians in High Dimensions 高维高斯混合学习

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 2015-03-01 DOI: 10.1145/2746539.2746616

Rong Ge, Qingqing Huang, S. Kakade

{"title":"Learning Mixtures of Gaussians in High Dimensions","authors":"Rong Ge, Qingqing Huang, S. Kakade","doi":"10.1145/2746539.2746616","DOIUrl":"https://doi.org/10.1145/2746539.2746616","url":null,"abstract":"Efficiently learning mixture of Gaussians is a fundamental problem in statistics and learning theory. Given samples coming from a random one out of k Gaussian distributions in Rn, the learning problem asks to estimate the means and the covariance matrices of these Gaussians. This learning problem arises in many areas ranging from the natural sciences to the social sciences, and has also found many ma- chine learning applications. Unfortunately, learning mixture of Gaussians is an information theoretically hard problem: in order to learn the parameters up to a reasonable accuracy, the number of samples required is exponential in the number of Gaussian components in the worst case. In this work, we show that provided we are in high enough dimensions, the class of Gaussian mixtures is learnable in its most general form under a smoothed analysis framework, where the parameters are randomly perturbed from an adversarial starting point. In particular, given samples from a mixture of Gaussians with randomly perturbed parameters, when n ≥ Ω(k2), we give an algorithm that learns the parameters with polynomial running time and using polynomial number of samples. The central algorithmic ideas consist of new ways to de- compose the moment tensor of the Gaussian mixture by exploiting its structural properties. The symmetries of this tensor are derived from the combinatorial structure of higher order moments of Gaussian distributions (sometimes referred to as Isserlis' theorem or Wick's theorem). We also develop new tools for bounding smallest singular values of structured random matrices, which could be useful in other smoothed analysis settings.","PeriodicalId":20566,"journal":{"name":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2015-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74555554","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: 117