Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing最新文献_第10页

Improved Quantum data analysis 改进的量子数据分析

Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2020-11-22 DOI: 10.1145/3406325.3451109

C. Badescu, R. O'Donnell

引用次数: 29

Improved dynamic algorithms for longest increasing subsequence 改进的最长递增子序列动态算法

Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2020-11-21 DOI: 10.1145/3406325.3451026

T. Kociumaka, Saeed Seddighin

{"title":"Improved dynamic algorithms for longest increasing subsequence","authors":"T. Kociumaka, Saeed Seddighin","doi":"10.1145/3406325.3451026","DOIUrl":"https://doi.org/10.1145/3406325.3451026","url":null,"abstract":"We study dynamic algorithms for the longest increasing subsequence (LIS) problem. A dynamic LIS algorithm maintains a sequence subject to operations of the following form arriving one by one: insert an element, delete an element, or substitute an element for another. After each update, the algorithm must report the length of the longest increasing subsequence of the current sequence. Our main contribution is the first exact dynamic LIS algorithm with sublinear update time. More precisely, we present a randomized algorithm that performs each operation in time Õ(n4/5) and, after each update, reports the answer to the LIS problem correctly with high probability. We use several novel techniques and observations for this algorithm that may find applications in future work. In the second part of the paper, we study approximate dynamic LIS algorithms, which are allowed to underestimate the solution size within a bounded multiplicative factor. In this setting, we give a deterministic (1−o(1))-approximation algorithm with update time O(no(1)). This result improves upon the previous work of Mitzenmacher and Seddighin (STOC’20) that provides an Ω(єO(1/є))-approximation algorithm with update time Õ(nє) for any є > 0.","PeriodicalId":132752,"journal":{"name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116318738","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: 12

Hop-constrained oblivious routing 跳数约束的无关路由

Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2020-11-20 DOI: 10.1145/3406325.3451098

M. Ghaffari, Bernhard Haeupler, Goran Zuzic

{"title":"Hop-constrained oblivious routing","authors":"M. Ghaffari, Bernhard Haeupler, Goran Zuzic","doi":"10.1145/3406325.3451098","DOIUrl":"https://doi.org/10.1145/3406325.3451098","url":null,"abstract":"We prove the existence of an oblivious routing scheme that is poly(logn)-competitive in terms of (congestion + dilation), thus resolving a well-known question in oblivious routing. Concretely, consider an undirected network and a set of packets each with its own source and destination. The objective is to choose a path for each packet, from its source to its destination, so as to minimize (congestion + dilation), defined as follows: The dilation is the maximum path hop-length, and the congestion is the maximum number of paths that include any single edge. The routing scheme obliviously and randomly selects a path for each packet independent of (the existence of) the other packets. Despite this obliviousness, the selected paths have (congestion + dilation) within a poly(logn) factor of the best possible value. More precisely, for any integer hop-bound h, this oblivious routing scheme selects paths of length at most h · poly(logn) and is poly(logn)-competitive in terms of congestion in comparison to the best possible congestion achievable via paths of length at most h hops. These paths can be sampled in polynomial time. This result can be viewed as an analogue of the celebrated oblivious routing results of R'acke [FOCS 2002, STOC 2008], which are O(logn)-competitive in terms of congestion, but are not competitive in terms of dilation.","PeriodicalId":132752,"journal":{"name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130893944","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: 18

Fully dynamic approximation of LIS in polylogarithmic time LIS在多对数时间内的完全动态逼近

Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2020-11-19 DOI: 10.1145/3406325.3451137

Paweł Gawrychowski, Wojciech Janczewski

{"title":"Fully dynamic approximation of LIS in polylogarithmic time","authors":"Paweł Gawrychowski, Wojciech Janczewski","doi":"10.1145/3406325.3451137","DOIUrl":"https://doi.org/10.1145/3406325.3451137","url":null,"abstract":"We revisit the problem of maintaining the longest increasing subsequence (LIS) of an array under (i) inserting an element, and (ii) deleting an element of an array. In a recent breakthrough, Mitzenmacher and Seddighin [STOC 2020] designed an algorithm that maintains an O((1/є)O(1/є))-approximation of LIS under both operations with worst-case update time Õ(nє), for any constant є>0 (Õ hides factors polynomial in logn, where n is the length of the input). We exponentially improve on their result by designing an algorithm that maintains an (1+є) approximation of LIS under both operations with worst-case update time Õ(є−5). Instead of working with the grid packing technique introduced by Mitzenmacher and Seddighin, we take a different approach building on a new tool that might be of independent interest: LIS sparsification. A particularly interesting consequence of our result is an improved solution for the so-called Erdős-Szekeres partitioning, in which we seek a partition of a given permutation of {1,2,…,n} into O(√n) monotone subsequences. This problem has been repeatedly stated as one of the natural examples in which we see a large gap between the decision-tree complexity and algorithmic complexity. The result of Mitzenmacher and Seddighin implies an O(n1+є) time solution for this problem, for any є>0. Our algorithm (in fact, its simpler decremental version) further improves this to Õ(n).","PeriodicalId":132752,"journal":{"name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","volume":"172 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134591376","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: 11

(Sub)Exponential advantage of adiabatic Quantum computation with no sign problem (下)无符号问题的绝热量子计算的指数优势

Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2020-11-18 DOI: 10.1145/3406325.3451060

Andr'as Gily'en, U. Vazirani

引用次数: 13

Towards tight bounds for spectral sparsification of hypergraphs 超图谱稀疏化的紧界问题

Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2020-11-12 DOI: 10.1145/3406325.3451061

M. Kapralov, Robert Krauthgamer, Jakab Tardos, Yuichi Yoshida

{"title":"Towards tight bounds for spectral sparsification of hypergraphs","authors":"M. Kapralov, Robert Krauthgamer, Jakab Tardos, Yuichi Yoshida","doi":"10.1145/3406325.3451061","DOIUrl":"https://doi.org/10.1145/3406325.3451061","url":null,"abstract":"Cut and spectral sparsification of graphs have numerous applications, including e.g. speeding up algorithms for cuts and Laplacian solvers. These powerful notions have recently been extended to hypergraphs, which are much richer and may offer new applications. However, the current bounds on the size of hypergraph sparsifiers are not as tight as the corresponding bounds for graphs. Our first result is a polynomial-time algorithm that, given a hypergraph on n vertices with maximum hyperedge size r, outputs an є-spectral sparsifier with O*(nr) hyperedges, where O* suppresses (є−1 logn)O(1) factors. This size bound improves the two previous bounds: O*(n3) [Soma and Yoshida, SODA’19] and O*(nr3) [Bansal, Svensson and Trevisan, FOCS’19]. Our main technical tool is a new method for proving concentration of the nonlinear analogue of the quadratic form of the Laplacians for hypergraph expanders. We complement this with lower bounds on the bit complexity of any compression scheme that (1+є)-approximates all the cuts in a given hypergraph, and hence also on the bit complexity of every є-cut/spectral sparsifier. These lower bounds are based on Ruzsa-Szemerédi graphs, and a particular instantiation yields an Ω(nr) lower bound on the bit complexity even for fixed constant є. In the case of hypergraph cut sparsifiers, this is tight up to polylogarithmic factors in n, due to recent result of [Chen, Khanna and Nagda, FOCS’20]. For spectral sparsifiers it narrows the gap to O*(r). Finally, for directed hypergraphs, we present an algorithm that computes an є-spectral sparsifier with O*(n2r3) hyperarcs, where r is the maximum size of a hyperarc. For small r, this improves over O*(n3) known from [Soma and Yoshida, SODA’19], and is getting close to the trivial lower bound of Ω(n2) hyperarcs.","PeriodicalId":132752,"journal":{"name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128813905","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: 22

A (2 + ε)-approximation algorithm for preemptive weighted flow time on a single machine 单机上优先加权流时间的(2 + ε)逼近算法

Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2020-11-11 DOI: 10.1145/3406325.3451075

Lars Rohwedder, Andreas Wiese

{"title":"A (2 + ε)-approximation algorithm for preemptive weighted flow time on a single machine","authors":"Lars Rohwedder, Andreas Wiese","doi":"10.1145/3406325.3451075","DOIUrl":"https://doi.org/10.1145/3406325.3451075","url":null,"abstract":"Weighted flow time is a fundamental and very well-studied objective function in scheduling. In this paper, we study the setting of a single machine with preemptions. The input consists of a set of jobs, characterized by their processing times, release times, and weights and we want to compute a (possibly preemptive) schedule for them. The objective is to minimize the sum of the weighted flow times of the jobs, where the flow time of a job is the time between its release date and its completion time. It had been a long-standing open problem to find a polynomial time O(1)-approximation algorithm for this setting. In a recent break-through result, Batra, Garg, and Kumar (FOCS 2018) found such an algorithm if the input data are polynomially bounded integers, and Feige, Kulkarni, and Li (SODA 2019) presented a black-box reduction to this setting. The resulting approximation ratio is a (not explicitly stated) constant which is at least 10000. In this paper we improve this ratio to 2+ε. The algorithm by Batra, Garg, and Kumar (FOCS 2018) reduces the problem to Demand MultiCut on trees and solves the resulting instances via LP-rounding and a dynamic program. Instead, we first reduce the problem to a (different) geometric problem while losing only a factor 1+ε, and then solve its resulting instances up to a factor of 2+ε by a dynamic program. In particular, our reduction ensures certain structural properties, thanks to which we do not need LP-rounding methods. We believe that our result makes substantial progress towards finding a PTAS for weighted flow time on a single machine.","PeriodicalId":132752,"journal":{"name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121854935","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: 6

Tree embeddings for hop-constrained network design 基于树嵌入的跳跃约束网络设计

Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2020-11-11 DOI: 10.1145/3406325.3451053

Bernhard Haeupler, D. E. Hershkowitz, Goran Zuzic

{"title":"Tree embeddings for hop-constrained network design","authors":"Bernhard Haeupler, D. E. Hershkowitz, Goran Zuzic","doi":"10.1145/3406325.3451053","DOIUrl":"https://doi.org/10.1145/3406325.3451053","url":null,"abstract":"Network design problems aim to compute low-cost structures such as routes, trees and subgraphs. Often, it is natural and desirable to require that these structures have small hop length or hop diameter. Unfortunately, optimization problems with hop constraints are much harder and less well understood than their hop-unconstrained counterparts. A significant algorithmic barrier in this setting is the fact that hop-constrained distances in graphs are very far from being a metric. We show that, nonetheless, hop-constrained distances can be approximated by distributions over ``partial tree metrics.'' We build this result into a powerful and versatile algorithmic tool which, similarly to classic probabilistic tree embeddings, reduces hop-constrained problems in general graphs to hop-unconstrained problems on trees. We then use this tool to give the first poly-logarithmic bicriteria approximations for the hop-constrained variants of many classic network design problems. These include Steiner forest, group Steiner tree, group Steiner forest, buy-at-bulk network design as well as online and oblivious versions of many of these problems.","PeriodicalId":132752,"journal":{"name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","volume":"124 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124831986","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: 11

A nearly-linear time algorithm for linear programs with small treewidth: a multiscale representation of robust central path 小树宽线性规划的近线性时间算法:鲁棒中心路径的多尺度表示

Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2020-11-10 DOI: 10.1145/3406325.3451056

Sally Dong, Y. Lee, Guanghao Ye

{"title":"A nearly-linear time algorithm for linear programs with small treewidth: a multiscale representation of robust central path","authors":"Sally Dong, Y. Lee, Guanghao Ye","doi":"10.1145/3406325.3451056","DOIUrl":"https://doi.org/10.1145/3406325.3451056","url":null,"abstract":"Arising from structural graph theory, treewidth has become a focus of study in fixed-parameter tractable algorithms. Many NP-hard problems are known to be solvable in O(n · 2O(τ)) time, where τ is the treewidth of the input graph. Analogously, many problems in P should be solvable in O(n · τO(1)) time; however, due to the lack of appropriate tools, only a few such results are currently known. In our paper, we show this holds for linear programs: Given a linear program of the form minAx=b,ℓ ≤ x≤ u c⊤ x whose dual graph GA has treewidth τ, and a corresponding width-τ tree decomposition, we show how to solve it in time O(n · τ2 log(1/ε)), where n is the number of variables and ε is the relative accuracy. When a tree decomposition is not given, we use existing techniques in vertex separators to obtain algorithms with O(n · τ4 log(1/ε)) and O(n · τ2 log(1/ε) + n1.5) run-times. Besides being the first of its kind, our algorithm has run-time nearly matching the fastest run-time for solving the sub-problem Ax=b (under the assumption that no fast matrix multiplication is used). We obtain these results by combining recent techniques in interior-point methods (IPMs), sketching, and a novel representation of the solution under a multiscale basis similar to the wavelet basis. This representation further yields the first IPM with o(rank(A)) time per iteration when the treewidth is small.","PeriodicalId":132752,"journal":{"name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133301435","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: 47

A theory of universal learning 普遍学习的理论

Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2020-11-09 DOI: 10.1145/3406325.3451087

O. Bousquet, Steve Hanneke, S. Moran, Ramon van Handel, A. Yehudayoff

{"title":"A theory of universal learning","authors":"O. Bousquet, Steve Hanneke, S. Moran, Ramon van Handel, A. Yehudayoff","doi":"10.1145/3406325.3451087","DOIUrl":"https://doi.org/10.1145/3406325.3451087","url":null,"abstract":"How quickly can a given class of concepts be learned from examples? It is common to measure the performance of a supervised machine learning algorithm by plotting its “learning curve”, that is, the decay of the error rate as a function of the number of training examples. However, the classical theoretical framework for understanding learnability, the PAC model of Vapnik-Chervonenkis and Valiant, does not explain the behavior of learning curves: the distribution-free PAC model of learning can only bound the upper envelope of the learning curves over all possible data distributions. This does not match the practice of machine learning, where the data source is typically fixed in any given scenario, while the learner may choose the number of training examples on the basis of factors such as computational resources and desired accuracy. In this paper, we study an alternative learning model that better captures such practical aspects of machine learning, but still gives rise to a complete theory of the learnable in the spirit of the PAC model. More precisely, we consider the problem of universal learning, which aims to understand the performance of learning algorithms on every data distribution, but without requiring uniformity over the distribution. The main result of this paper is a remarkable trichotomy: there are only three possible rates of universal learning. More precisely, we show that the learning curves of any given concept class decay either at an exponential, linear, or arbitrarily slow rates. Moreover, each of these cases is completely characterized by appropriate combinatorial parameters, and we exhibit optimal learning algorithms that achieve the best possible rate in each case. For concreteness, we consider in this paper only the realizable case, though analogous results are expected to extend to more general learning scenarios.","PeriodicalId":132752,"journal":{"name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121146464","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: 34