Submodular Functions and Perfect Graphs

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-15 DOI:10.1287/moor.2021.0302

Tara Abrishami, Maria Chudnovsky, Cemil Dibek, Kristina Vušković

引用次数: 0

Abstract

We give a combinatorial polynomial-time algorithm to find a maximum weight independent set in perfect graphs of bounded degree that do not contain a prism or a hole of length four as an induced subgraph. An even pair in a graph is a pair of vertices all induced paths between which are even. An even set is a set of vertices every two of which are an even pair. We show that every perfect graph that does not contain a prism or a hole of length four as an induced subgraph has a balanced separator which is the union of a bounded number of even sets, where the bound depends only on the maximum degree of the graph. This allows us to solve the maximum weight independent set problem using the well-known submodular function minimization algorithm.Funding: This work was supported by the Engineering and Physical Sciences Research Council [Grant EP/V002813/1]; the National Science Foundation [Grants DMS-1763817, DMS-2120644, and DMS-2303251]; and Alexander von Humboldt-Stiftung.

查看原文本刊更多论文

亚模态函数与完美图形

我们给出了一种组合多项式时间算法，可以在不包含长度为四的棱或洞作为诱导子图的有界度完美图中找到最大权重独立集。图中的偶数对是指一对顶点之间的所有诱导路径都是偶数。偶数集是每两个顶点都是偶数对的顶点集。我们证明，每一个不包含棱柱或长度为四的洞的完美图的诱导子图都有一个平衡分隔符，它是有界数的偶数集的联合，而界数只取决于图的最大度。这样，我们就可以使用著名的子模函数最小化算法来解决最大权重独立集问题：本研究得到了工程与物理科学研究委员会 [EP/V002813/1 号基金]、美国国家科学基金会 [DMS-1763817 号基金、DMS-2120644 号基金和 DMS-2303251 号基金] 以及 Alexander von Humboldt-Stiftung 的资助。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.