XNLP-Completeness for Parameterized Problems on Graphs with a Linear Structure

IF 0.9 4区计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Algorithmica Pub Date : 2024-11-04 DOI:10.1007/s00453-024-01274-9

Hans L. Bodlaender, Carla Groenland, Hugo Jacob, Lars Jaffke, Paloma T. Lima

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引用次数: 0

Abstract

In this paper, we showcase the class XNLP as a natural place for many hard problems parameterized by linear width measures. This strengthens existing W[1]-hardness proofs for these problems, since XNLP-hardness implies W[t]-hardness for all t. It also indicates, via a conjecture by Pilipczuk and Wrochna (ACM Trans Comput Theory 9:1–36, 2018), that any XP algorithm for such problems is likely to require XP space. In particular, we show XNLP-completeness for natural problems parameterized by pathwidth, linear clique-width, and linear mim-width. The problems we consider are Independent Set, Dominating Set, Odd Cycle Transversal, (q-)Coloring, Max Cut, Maximum Regular Induced Subgraph, Feedback Vertex Set, Capacitated (Red-Blue) Dominating Set, Capacitated Vertex Cover and Bipartite Bandwidth.

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在本文中，我们展示了 XNLP 类是许多以线性宽度度量为参数的难题的天然栖息地。这加强了对这些问题的现有 W[1]-hardness 证明，因为 XNLP -hardness 意味着对所有 t 的 W[t]-hardness 证明。它还通过 Pilipczuk 和 Wrochna 的猜想（ACM Trans Comput Theory 9:1-36, 2018）表明，针对此类问题的任何 XP 算法都可能需要 XP 空间。具体而言，我们展示了以路径宽度、线性clique-width和线性mim-width为参数的自然问题的XNLP完备性。我们考虑的问题包括独立集、支配集、奇数循环横向、（q-）着色、最大切割、最大规则诱导子图、反馈顶点集、有容乃大（红蓝）支配集、有容乃大顶点覆盖和双方形带宽。

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

Algorithmica 工程技术-计算机：软件工程

CiteScore

2.80

自引率

9.10%

发文量

158

审稿时长

12 months

期刊介绍： Algorithmica is an international journal which publishes theoretical papers on algorithms that address problems arising in practical areas, and experimental papers of general appeal for practical importance or techniques. The development of algorithms is an integral part of computer science. The increasing complexity and scope of computer applications makes the design of efficient algorithms essential. Algorithmica covers algorithms in applied areas such as: VLSI, distributed computing, parallel processing, automated design, robotics, graphics, data base design, software tools, as well as algorithms in fundamental areas such as sorting, searching, data structures, computational geometry, and linear programming. In addition, the journal features two special sections: Application Experience, presenting findings obtained from applications of theoretical results to practical situations, and Problems, offering short papers presenting problems on selected topics of computer science.