最大切割和半定秩

IF 0.8 4区管理学 Q4 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Operations Research Letters Pub Date : 2024-01-17 DOI:10.1016/j.orl.2024.107067

Renee Mirka, David P. Williamson

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引用次数: 0

摘要

本文探讨了半定量程序（SDP）、矩阵秩和图形最大切割之间的关系。利用 SDP 的互补松弛条件，我们通过证明存在秩为 n-1 的最优对偶解，研究了与最大切割对应的秩 1 可行解何时是 Goemans-Williamson 最大切割 SDP 的唯一最优解。我们的结果考虑了连通的二叉图和具有多个最大切点的图。最后，我们对一般图提出了一个猜想。

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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Max cut and semidefinite rank

This paper considers the relationship between semidefinite programs (SDPs), matrix rank, and maximum cuts of graphs. Utilizing complementary slackness conditions for SDPs, we investigate when the rank 1 feasible solution corresponding to a max cut is the unique optimal solution to the Goemans-Williamson max cut SDP by showing the existence of an optimal dual solution with rank $n - 1$ . Our results consider connected bipartite graphs and graphs with multiple max cuts. We conclude with a conjecture for general graphs.

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来源期刊

Operations Research Letters 管理科学-运筹学与管理科学

CiteScore

2.10

自引率

9.10%

发文量

111

审稿时长

83 days

期刊介绍： Operations Research Letters is committed to the rapid review and fast publication of short articles on all aspects of operations research and analytics. Apart from a limitation to eight journal pages, quality, originality, relevance and clarity are the only criteria for selecting the papers to be published. ORL covers the broad field of optimization, stochastic models and game theory. Specific areas of interest include networks, routing, location, queueing, scheduling, inventory, reliability, and financial engineering. We wish to explore interfaces with other fields such as life sciences and health care, artificial intelligence and machine learning, energy distribution, and computational social sciences and humanities. Our traditional strength is in methodology, including theory, modelling, algorithms and computational studies. We also welcome novel applications and concise literature reviews.