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

H. Bodlaender, C. Groenland, Hugo Jacob
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引用次数: 9

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 [ToCT 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, and Bipartite Bandwidth.
线性结构图上参数化问题的xnlp完备性
在本文中,我们展示了类XNLP作为许多由线性宽度度量参数化的难题的自然场所。这加强了现有的针对这些问题的$W[1]$硬度证明,因为xnlp -硬度意味着所有$t$的$W[t]$硬度。它还表明,通过Pilipczuk和Wrochna [ToCT 2018]的猜想,任何XP算法对于这类问题都可能需要XP空间。特别地,我们展示了由路径宽度、线性团宽度和线性最小宽度参数化的自然问题的xnlp完备性。我们考虑的问题有:独立集、支配集、奇环截线、($q$-)着色、最大切、最大正则诱导子图、反馈顶点集、有能力(红蓝)支配集和二部带宽。
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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