SIAM Journal on Computing最新文献_第8页

Quantum Speedup for Graph Sparsification, Cut Approximation, and Laplacian Solving 图稀疏化、切近似和拉普拉斯求解的量子加速

IF 1.6 3区计算机科学

SIAM Journal on Computing Pub Date : 2022-12-20 DOI: 10.1137/21m1391018

Simon Apers, Ronald de Wolf

{"title":"Quantum Speedup for Graph Sparsification, Cut Approximation, and Laplacian Solving","authors":"Simon Apers, Ronald de Wolf","doi":"10.1137/21m1391018","DOIUrl":"https://doi.org/10.1137/21m1391018","url":null,"abstract":"SIAM Journal on Computing, Volume 51, Issue 6, Page 1703-1742, December 2022. <br/> Abstract. Graph sparsification underlies a large number of algorithms, ranging from approximation algorithms for cut problems to solvers for linear systems in the graph Laplacian. In its strongest form, “spectral sparsification” reduces the number of edges to near-linear in the number of nodes, while approximately preserving the cut and spectral structure of the graph. In this work we demonstrate a polynomial quantum speedup for spectral sparsification and many of its applications. In particular, we give a quantum algorithm that, given a weighted graph with [math] nodes and [math] edges, outputs a classical description of an [math]-spectral sparsifier in sublinear time [math]. This contrasts with the optimal classical complexity [math]. We also prove that our quantum algorithm is optimal up to polylog-factors. The algorithm builds on a string of existing results on sparsification, graph spanners, quantum algorithms for shortest paths, and efficient constructions for [math]-wise independent random strings. Our algorithm implies a quantum speedup for solving Laplacian systems and for approximating a range of cut problems such as min cut and sparsest cut.","PeriodicalId":49532,"journal":{"name":"SIAM Journal on Computing","volume":"22 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138520759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Subexponential Parameterized Algorithms for Planar and Apex-Minor-Free Graphs via Low Treewidth Pattern Covering 基于低树宽模式覆盖的平面图和顶点无次图的亚指数参数化算法

IF 1.6 3区计算机科学

SIAM Journal on Computing Pub Date : 2022-12-20 DOI: 10.1137/19m1262504

Fedor V. Fomin, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michał Pilipczuk, Saket Saurabh

{"title":"Subexponential Parameterized Algorithms for Planar and Apex-Minor-Free Graphs via Low Treewidth Pattern Covering","authors":"Fedor V. Fomin, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michał Pilipczuk, Saket Saurabh","doi":"10.1137/19m1262504","DOIUrl":"https://doi.org/10.1137/19m1262504","url":null,"abstract":"SIAM Journal on Computing, Volume 51, Issue 6, Page 1866-1930, December 2022. <br/> Abstract. We prove the following theorem. Given a planar graph [math] and an integer [math], it is possible in polynomial time to randomly sample a subset [math] of vertices of [math] with the following properties: [math] induces a subgraph of [math] of treewidth [math], and for every connected subgraph [math] of [math] on at most [math] vertices, the probability that [math] covers the whole vertex set of [math] is at least [math], where [math] is the number of vertices of [math]. Together with standard dynamic programming techniques for graphs of bounded treewidth, this result gives a versatile technique for obtaining (randomized) subexponential-time parameterized algorithms for problems on planar graphs, usually with running time bound [math]. The technique can be applied to problems expressible as searching for a small, connected pattern with a prescribed property in a large host graph; examples of such problems include Directed [math]-Path, Weighted [math]-Path, Vertex Cover Local Search, and Subgraph Isomorphism, among others. Up to this point, it was open whether these problems could be solved in subexponential parameterized time on planar graphs, because they are not amenable to the classic technique of bidimensionality. Furthermore, all our results hold in fact on any class of graphs that exclude a fixed apex graph as a minor, in particular on graphs embeddable in any fixed surface.","PeriodicalId":49532,"journal":{"name":"SIAM Journal on Computing","volume":"18 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138520764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Relaxed Locally Correctable Codes with Nearly-Linear Block Length and Constant Query Complexity 具有近似线性块长度和恒定查询复杂度的松弛局部可纠错码

IF 1.6 3区计算机科学

SIAM Journal on Computing Pub Date : 2022-12-16 DOI: 10.1137/20m135515x

Alessandro Chiesa, Tom Gur, Igor Shinkar

{"title":"Relaxed Locally Correctable Codes with Nearly-Linear Block Length and Constant Query Complexity","authors":"Alessandro Chiesa, Tom Gur, Igor Shinkar","doi":"10.1137/20m135515x","DOIUrl":"https://doi.org/10.1137/20m135515x","url":null,"abstract":"SIAM Journal on Computing, Volume 51, Issue 6, Page 1839-1865, December 2022. <br/> Abstract. Locally correctable codes (LCCs) are error correcting codes [math] which admit local algorithms that correct any individual symbol of a corrupted codeword via a minuscule number of queries. For systematic codes, this notion is stronger than that of locally decodable codes (LDCs), where the goal is to only recover individual symbols of the message. One of the central problems in algorithmic coding theory is to construct [math]-query LCCs and LDCs with minimal block length. Alas, state-of-the-art of such codes requires super-polynomial block length to admit [math]-query algorithms for local correction and decoding, despite much attention during the last two decades. The study of relaxed LCCs and LDCs, which allow the correction algorithm to abort (but not err) on a small fraction of the locations, provides a way to circumvent this barrier. This relaxation turned out to allow constant-query correcting and decoding algorithms for codes with polynomial block length. Focusing on local correction, Gur, Ramnarayan, and Rothblum [Proceedings of the 9th Innovations in Theoretical Computer Science Conference, ITCS’18, 2018, pp. 1–27] showed that there exist [math]-query relaxed LCCs that achieve nearly-quartic block length [math], for an arbitrarily small constant [math]. We construct an [math]-query relaxed LCC with nearly-linear block length [math], for an arbitrarily small constant [math]. This significantly narrows the gap between the lower bound which states that there are no [math]-query relaxed LCCs with block length [math]. In particular, our construction matches the parameters achieved by Ben-Sasson et al. [SIAM J. Comput., 36 (2006), pp. 889–974], who constructed relaxed LDCs with the same parameters. This resolves an open problem raised by Gur, Ramnarayan, and Rothblum [Proceedings of the 9th Innovations in Theoretical Computer Science Conference, ITCS’18, 2018, pp. 1–27].","PeriodicalId":49532,"journal":{"name":"SIAM Journal on Computing","volume":"11 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138520739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Corrigendum: Explicit Construction of a Small Epsilon-Net for Linear Threshold Functions 更正:线性阈值函数的小Epsilon-Net的显式构造

IF 1.6 3区计算机科学

SIAM Journal on Computing Pub Date : 2022-10-31 DOI: 10.1137/20m1310321

Yuval Rabani, Amir Shpilka

引用次数: 0

Unit Capacity Maxflow in Almost $m^{4/3}$ Time 单位容量的最大流量几乎$m^{4/3}$时间

IF 1.6 3区计算机科学

SIAM Journal on Computing Pub Date : 2022-04-18 DOI: 10.1137/20m1383525

Tarun Kathuria, Yang P. Liu, Aaron Sidford

引用次数: 9

Performance of Johnson--Lindenstrauss Transform for $k$-Means and $k$-Medians Clustering $k$均值和$k$中位数聚类的Johnson- Lindenstrauss变换性能

IF 1.6 3区计算机科学

SIAM Journal on Computing Pub Date : 2022-03-14 DOI: 10.1137/20m1330701

K. Makarychev, Yury Makarychev, Ilya P. Razenshteyn

引用次数: 19

The Complexity of Necklace Splitting, Consensus-Halving, and Discrete Ham Sandwich 项链分割、共识减半和离散火腿三明治的复杂性

IF 1.6 3区计算机科学

SIAM Journal on Computing Pub Date : 2022-02-28 DOI: 10.1137/20m1312678

Aris Filos-Ratsikas, Paul W Goldberg

引用次数: 5

Distributed Exact Weighted All-Pairs Shortest Paths in Randomized Near-Linear Time 随机近线性时间下的分布精确加权全对最短路径

IF 1.6 3区计算机科学

SIAM Journal on Computing Pub Date : 2021-11-23 DOI: 10.1137/20m1312782

A. Bernstein, Danupon Nanongkai

引用次数: 1

ERROR-CORRECTING DATA STRUCTURES ∗ 纠错数据结构*

IF 1.6 3区计算机科学

SIAM Journal on Computing Pub Date : 2013-01-10 DOI: 10.1137/110834949

Victor Chen, E. Grigorescu, Ronald de Wolf

引用次数: 0

Unifying the Landscape of Cell-Probe Lower Bounds 统一细胞探针下界的景观

IF 1.6 3区计算机科学

SIAM Journal on Computing Pub Date : 2011-05-01 DOI: 10.1137/09075336X

Mihai Pa caron, traşcu

{"title":"Unifying the Landscape of Cell-Probe Lower Bounds","authors":"Mihai Pa caron, traşcu","doi":"10.1137/09075336X","DOIUrl":"https://doi.org/10.1137/09075336X","url":null,"abstract":"We show that a large fraction of the data-structure lower bounds known today in fact follow by reduction from the communication complexity of lopsided (asymmetric) set disjointness. This includes lower bounds for (i) high-dimensional problems, where the goal is to show large space lower bounds; (ii) constant-dimensional geometric problems, where the goal is to bound the query time for space $O(ncdotmathrm{polylog}n)$; and (iii) dynamic problems, where we are looking for a trade-off between query and update time. (In the last case, our bounds are slightly weaker than the originals, losing a $lglg n$ factor.) Our reductions also imply the following new results: (i) an $Omega(lg n/lglg n)$ bound for four-dimensional range reporting, given space $O(ncdotmathrm{polylog}n)$ (this is quite timely, since a recent result [Y. Nekrich, in Proceedings of the 23rd ACM Symposium on Computational Geometry (SoCG), 2007, pp. 344-353] solved three-dimensional reporting in $O(lg^2lg n)$ time, raising the prospect that higher dimensions could also be easy); (ii) a tight space lower bound for the partial match problem, for constant query time; and (iii) the first lower bound for reachability oracles. In the process, we prove optimal randomized lower bounds for lopsided set disjointness.","PeriodicalId":49532,"journal":{"name":"SIAM Journal on Computing","volume":"42 4","pages":"827-847"},"PeriodicalIF":1.6,"publicationDate":"2011-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1137/09075336X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72390773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 93