Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)最新文献_第6页

A Simple Semi-Streaming Algorithm for Global Minimum Cuts 一种简单的半流全局最小割算法

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2021-01-01 DOI: 10.1137/1.9781611976496.19

Sepehr Assadi, Aditi Dudeja

引用次数: 9

Floors and Ceilings in Divide-and-Conquer Recurrences 分治法递归中的地板和天花板

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2021-01-01 DOI: 10.1137/1.9781611976496.15

William Kuszmaul, C. Leiserson

引用次数: 3

Hutch++: Optimal Stochastic Trace Estimation. Hutch++:最优随机轨迹估计。

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2021-01-01 DOI: 10.1137/1.9781611976496.16

Raphael A Meyer, Cameron Musco, Christopher Musco, David P Woodruff

{"title":"Hutch++: Optimal Stochastic Trace Estimation.","authors":"Raphael A Meyer, Cameron Musco, Christopher Musco, David P Woodruff","doi":"10.1137/1.9781611976496.16","DOIUrl":"https://doi.org/10.1137/1.9781611976496.16","url":null,"abstract":"We study the problem of estimating the trace of a matrix A that can only be accessed through matrix-vector multiplication. We introduce a new randomized algorithm, Hutch++, which computes a (1 ± ε) approximation to tr( A ) for any positive semidefinite (PSD) A using just O(1/ε) matrix-vector products. This improves on the ubiquitous Hutchinson's estimator, which requires O(1/ε 2) matrix-vector products. Our approach is based on a simple technique for reducing the variance of Hutchinson's estimator using a low-rank approximation step, and is easy to implement and analyze. Moreover, we prove that, up to a logarithmic factor, the complexity of Hutch++ is optimal amongst all matrix-vector query algorithms, even when queries can be chosen adaptively. We show that it significantly outperforms Hutchinson's method in experiments. While our theory requires A to be positive semidefinite, empirical gains extend to applications involving non-PSD matrices, such as triangle estimation in networks.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"2021 ","pages":"142-155"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8553228/pdf/nihms-1696966.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39580860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 73

Dispersion for Intervals: A Geometric Approach 区间色散:一种几何方法

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2021-01-01 DOI: 10.1137/1.9781611976496.4

T. Biedl, A. Lubiw, Anurag Murty Naredla, Peter Dominik Ralbovsky, Graeme Stroud

引用次数: 2

Simple dynamic algorithms for Maximal Independent Set, Maximum Flow and Maximum Matching 最大独立集、最大流量和最大匹配的简单动态算法

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2021-01-01 DOI: 10.1137/1.9781611976496.10

Manoj Gupta, Shahbaz Khan

引用次数: 3

An Auction Algorithm for Bipartite Matching in Streaming and Massively Parallel Computation Models 流计算和大规模并行计算模型中二部匹配的拍卖算法

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2021-01-01 DOI: 10.1137/1.9781611976496.18

Sepehr Assadi, S. C. Liu, R. Tarjan

引用次数: 17

Communication Efficient Coresets for Maximum Matching 最大匹配的通信高效核心集

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2020-11-12 DOI: 10.1137/1.9781611976496.17

Michael Kapralov, Gilbert Maystre, Jakab Tardos

引用次数: 2

Recursive Random Contraction Revisited 再次回顾递归随机收缩

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2020-10-29 DOI: 10.1137/1.9781611976496.7

David R Karger, David P. Williamson

引用次数: 1

Unifying Matrix Data Structures: Simplifying and Speeding up Iterative Algorithms 统一矩阵数据结构:简化和加速迭代算法

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2020-10-26 DOI: 10.1137/1.9781611976496.1

J. V. D. Brand

{"title":"Unifying Matrix Data Structures: Simplifying and Speeding up Iterative Algorithms","authors":"J. V. D. Brand","doi":"10.1137/1.9781611976496.1","DOIUrl":"https://doi.org/10.1137/1.9781611976496.1","url":null,"abstract":"Many algorithms use data structures that maintain properties of matrices undergoing some changes. The applications are wide-ranging and include for example matchings, shortest paths, linear programming, semi-definite programming, convex hull and volume computation. Given the wide range of applications, the exact property these data structures must maintain varies from one application to another, forcing algorithm designers to invent them from scratch or modify existing ones. Thus it is not surprising that these data structures and their proofs are usually tailor-made for their specific application and that maintaining more complicated properties results in more complicated proofs. \u0000In this paper we present a unifying framework that captures a wide range of these data structures. The simplicity of this framework allows us to give short proofs for many existing data structures regardless of how complicated the to be maintained property is. We also show how the framework can be used to speed up existing iterative algorithms, such as the simplex algorithm. \u0000More formally, consider any rational function $f(A_1,...,A_d)$ with input matrices $A_1,...,A_d$. We show that the task of maintaining $f(A_1,...,A_d)$ under updates to $A_1,...,A_d$ can be reduced to the much simpler problem of maintaining some matrix inverse $M^{-1}$ under updates to $M$. The latter is a well studied problem called dynamic matrix inverse. By applying our reduction and using known algorithms for dynamic matrix inverse we can obtain fast data structures and iterative algorithms for much more general problems.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"42 1","pages":"1-13"},"PeriodicalIF":0.0,"publicationDate":"2020-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89881041","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: 16

Recognizing (Unit) Interval Graphs by Zigzag Graph Searches 用z形图搜索识别(单位)间隔图

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2020-10-07 DOI: 10.1137/1.9781611976496.11

Yixin Cao

引用次数: 2