{"title":"Fully Dynamic Electrical Flows: Sparse Maxflow Faster Than Goldberg–Rao","authors":"Yu Gao, Yang Liu, Richard Peng","doi":"10.1137/22m1476666","DOIUrl":null,"url":null,"abstract":"We give an algorithm for computing exact maximum flows on graphs with edges and integer capacities in the range in time. We use to suppress logarithmic factors in . For sparse graphs with polynomially bounded integer capacities, this is the first improvement over the time bound from Goldberg and Rao [J. ACM, 45 (1998), pp. 783–797]. Our algorithm revolves around dynamically maintaining the augmenting electrical flows at the core of the interior point method based algorithm from Ma̧dry [Proceedings of the 57th IEEE Annual Symposium on Foundations of Computer Science, 2016, pp. 593–602]. This entails designing data structures that, in limited settings, return edges with large electric energy in a graph undergoing resistance updates.","PeriodicalId":49532,"journal":{"name":"SIAM Journal on Computing","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/22m1476666","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
We give an algorithm for computing exact maximum flows on graphs with edges and integer capacities in the range in time. We use to suppress logarithmic factors in . For sparse graphs with polynomially bounded integer capacities, this is the first improvement over the time bound from Goldberg and Rao [J. ACM, 45 (1998), pp. 783–797]. Our algorithm revolves around dynamically maintaining the augmenting electrical flows at the core of the interior point method based algorithm from Ma̧dry [Proceedings of the 57th IEEE Annual Symposium on Foundations of Computer Science, 2016, pp. 593–602]. This entails designing data structures that, in limited settings, return edges with large electric energy in a graph undergoing resistance updates.
给出了在时间范围内具有边和整数容量的图上精确计算最大流的算法。我们用来抑制对数因子。对于具有多项式有界整数容量的稀疏图，这是Goldberg和Rao [J]在时间限制上的第一个改进。ACM, 45 (1998)， pp. 783-797。我们的算法围绕动态维持基于Ma ' o dry的内点法算法核心的增强电流展开[第57届IEEE计算机科学基础年度研讨会论文集，2016,pp. 593-602]。这需要设计数据结构，在有限的设置下，在进行阻力更新的图中返回具有大电能的边。
期刊介绍：
The SIAM Journal on Computing aims to provide coverage of the most significant work going on in the mathematical and formal aspects of computer science and nonnumerical computing. Submissions must be clearly written and make a significant technical contribution. Topics include but are not limited to analysis and design of algorithms, algorithmic game theory, data structures, computational complexity, computational algebra, computational aspects of combinatorics and graph theory, computational biology, computational geometry, computational robotics, the mathematical aspects of programming languages, artificial intelligence, computational learning, databases, information retrieval, cryptography, networks, distributed computing, parallel algorithms, and computer architecture.
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