Exploring Clique Transversal Problems for d-degenerate Graphs with Fixed d: From Polynomial-Time Solvability to Parameterized Complexity

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-04 DOI:10.3390/axioms13060382

Chuan-Min Lee

引用次数: 0

Abstract

This paper explores the computational challenges of clique transversal problems in d-degenerate graphs, which are commonly encountered across theoretical computer science and various network applications. We examine d-degenerate graphs to highlight their utility in representing sparse structures and assess several variations of clique transversal problems, including the b-fold and {b}-clique transversal problems, focusing on their computational complexities for different graph categories. Our analysis identifies that certain instances of these problems are polynomial-time solvable in specific graph classes, such as 1-degenerate or 2-degenerate graphs. However, for d-degenerate graphs where d≥2, these problems generally escalate to NP-completeness. We also explore the parameterized complexity, pinpointing specific conditions that render these problems fixed-parameter tractable.

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探索具有固定 d 的 d 退化图的簇横向问题：从多项式时间可解性到参数化复杂性

本文探讨了在理论计算机科学和各种网络应用中经常遇到的 d-退化图中的簇横向问题的计算挑战。我们研究了 denerate 图，以突出它们在表示稀疏结构方面的实用性，并评估了簇横向问题的几种变体，包括 b-fold 和 {b}-clique 横向问题，重点关注它们在不同图类中的计算复杂性。我们的分析表明，这些问题的某些实例在特定图类中是可以用多项式时间求解的，例如 1 退化图或 2 退化图。然而，对于 d≥2 的 d 退化图，这些问题一般会升级到 NP 完备性。我们还探索了参数化复杂性，指出了使这些问题具有固定参数可操作性的特定条件。

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

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.