Greediness is not always a vice: Efficient discovery algorithms for assignment problems

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2025-07-11 DOI:10.1016/j.dam.2025.06.020

Romaric Duvignau , Noël Gillet , Ralf Klasing

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引用次数: 0

Abstract

Finding a maximum-weight matching is a classical and well-studied problem in computer science, solvable in cubic time in general graphs. We consider the specialization called assignment problem where the input is a bipartite graph, and introduce in this work the “discovery” variant considering edge weights that are not provided as input but must be queried, requiring additional and costly computations. We develop discovery algorithms here to minimize the number of queried weights while providing guarantees on the computed solution. In this work, we first show the inherent challenges of designing discovery algorithms for general assignment problems. We then provide and analyze several efficient greedy algorithms that can make use of natural assumptions about the order in which the nodes are processed by the algorithms. Our motivations for exploring this problem stem from finding practical solutions to a variation of maximum weight matching in bipartite hypergraphs, a problem recently emerging in the formation of peer-to-peer energy-sharing communities.

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贪婪并不总是一种恶习：分配问题的高效发现算法

在计算机科学中，寻找最大权重匹配是一个经典且研究得很充分的问题，在一般图中可以在三次时间内解决。我们考虑了称为分配问题的专门化，其中输入是一个二部图，并在这项工作中引入了考虑边缘权重的“发现”变体，这些边缘权重不作为输入提供，但必须查询，需要额外和昂贵的计算。我们在这里开发了发现算法，以最小化查询权重的数量，同时保证计算出的解决方案。在这项工作中，我们首先展示了为一般分配问题设计发现算法的固有挑战。然后，我们提供并分析了几种有效的贪婪算法，这些算法可以利用关于节点被算法处理的顺序的自然假设。我们探索这个问题的动机源于寻找二部超图中最大权重匹配变化的实际解决方案，这是最近在点对点能量共享社区形成中出现的一个问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.