Fast primal-dual update against local weight update in linear assignment problem and its application

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters Pub Date : 2023-08-05 DOI:10.1016/j.ipl.2023.106432

Kohei Morita , Shinya Shiroshita , Yutaro Yamaguchi , Yu Yokoi

{"title":"Fast primal-dual update against local weight update in linear assignment problem and its application","authors":"Kohei Morita , Shinya Shiroshita , Yutaro Yamaguchi , Yu Yokoi","doi":"10.1016/j.ipl.2023.106432","DOIUrl":null,"url":null,"abstract":"<div>We consider a dynamic situation in the weighted bipartite matching problem: edge weights in the input graph are repeatedly updated and we are asked to maintain an optimal matching at any moment. A trivial approach is to compute an optimal matching from scratch each time an update occurs. In this paper, we show that if each update occurs locally around a single vertex, then a single execution of Dijkstra's algorithm is sufficient to preserve optimality with the aid of a dual solution. As an application of our result, we provide a faster implementation of the envy-cycle procedure for finding an envy-free allocation of indivisible items. Our algorithm runs in <math><mi>O</mi><mo>(</mo><mi>m</mi><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math> time, while the known bound of the original one is <math><mi>O</mi><mo>(</mo><mi>m</mi><msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math>, where n and m denote the numbers of agents and items, respectively.</div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"183 ","pages":"Article 106432"},"PeriodicalIF":0.7000,"publicationDate":"2023-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Information Processing Letters","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0020019023000753","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}

引用次数: 3

Abstract

We consider a dynamic situation in the weighted bipartite matching problem: edge weights in the input graph are repeatedly updated and we are asked to maintain an optimal matching at any moment. A trivial approach is to compute an optimal matching from scratch each time an update occurs. In this paper, we show that if each update occurs locally around a single vertex, then a single execution of Dijkstra's algorithm is sufficient to preserve optimality with the aid of a dual solution. As an application of our result, we provide a faster implementation of the envy-cycle procedure for finding an envy-free allocation of indivisible items. Our algorithm runs in $O (m n^{2})$ time, while the known bound of the original one is $O (m n^{3})$ , where n and m denote the numbers of agents and items, respectively.

查看原文本刊更多论文

线性分配问题中针对局部权值更新的快速原对偶更新及其应用

我们考虑加权二部分匹配问题中的一种动态情况：输入图中的边缘权重被重复更新，并且我们被要求在任何时刻保持最优匹配。一种简单的方法是每次更新时从头开始计算最佳匹配。在本文中，我们证明了如果每次更新都发生在单个顶点附近，那么Dijkstra算法的一次执行就足以在对偶解的帮助下保持最优性。作为我们结果的应用，我们提供了嫉妒循环程序的更快实现，以找到不可分割项目的无嫉妒分配。我们的算法在O（mn2）时间内运行，而原始算法的已知边界是O（mn3），其中n和m分别表示代理和项目的数量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Information Processing Letters 工程技术-计算机：信息系统

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

7.3 months

期刊介绍： Information Processing Letters invites submission of original research articles that focus on fundamental aspects of information processing and computing. This naturally includes work in the broadly understood field of theoretical computer science; although papers in all areas of scientific inquiry will be given consideration, provided that they describe research contributions credibly motivated by applications to computing and involve rigorous methodology. High quality experimental papers that address topics of sufficiently broad interest may also be considered. Since its inception in 1971, Information Processing Letters has served as a forum for timely dissemination of short, concise and focused research contributions. Continuing with this tradition, and to expedite the reviewing process, manuscripts are generally limited in length to nine pages when they appear in print.