一种确定多目标整数网络流问题所有支持有效解的输出多项式时间算法

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2025-06-20 DOI:10.1016/j.dam.2025.06.001

David Könen, Michael Stiglmayr

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引用次数: 0

摘要

本文研究了线性多目标整数最小成本流问题的所有支持有效解的枚举问题。它导出了一个输出多项式时间算法来确定MOIMCF问题的所有支持的有效解。这是在输出多项式时间内解决这个一般问题的第一种方法。此外，我们证明了一个输出多项式时间算法的存在性，该算法可以排除具有固定数量d≥3个目标的MOIMCF问题的所有弱支持非支配向量（或所有弱支持有效解），除非P=NP。

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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An output-polynomial time algorithm to determine all supported efficient solutions for multi-objective integer network flow problems

This paper addresses the problem of enumerating all supported efficient solutions for a linear multi-objective integer minimum cost flow problem (MOIMCF). It derives an output-polynomial time algorithm to determine all supported efficient solutions for MOIMCF problems. This is the first approach to solve this general problem in output-polynomial time. Moreover, we prove that the existence of an output-polynomial time algorithm to determine all weakly supported nondominated vectors (or all weakly supported efficient solutions) for a MOIMCF problem with a fixed number of

d \geq 3

objectives can be excluded unless

P = NP

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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.