Long directed detours: Reduction to 2-Disjoint Paths

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters Pub Date : 2024-03-13 DOI:10.1016/j.ipl.2024.106491

Ashwin Jacob, Michał Włodarczyk, Meirav Zehavi

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引用次数: 0

Abstract

In the Longest $(s, t)$ -Detour problem, we look for an $(s, t)$ -path that is at least k vertices longer than a shortest one. We study the parameterized complexity of Longest $(s, t)$ -Detour when parameterized by k: this falls into the research paradigm of ‘parameterization above guarantee’. Whereas the problem is known to be fixed-parameter tractable (FPT) on undirected graphs, the status of Longest $(s, t)$ -Detour on directed graphs remains highly unclear: it is not even known to be solvable in polynomial time for $k = 1$ . Recently, Fomin et al. made progress in this direction by showing that the problem is FPT on every class of directed graphs where the 3-Disjoint Paths problem is solvable in polynomial time. We improve upon their result by weakening this assumption: we show that only a polynomial-time algorithm for 2-Disjoint Paths is required.

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长定向迂回：还原为二叉路径

在这个问题中，我们要寻找一条至少比最短路径长一个顶点的路径。我们研究的是当参数化为：时的参数化复杂度，这属于 "参数化高于保证 "的研究范式。虽然这个问题在无向图上是已知的固定参数可处理（FPT）问题，但在有向图上的情况仍然非常不清楚：甚至不知道......的多项式时间内是否可以求解。最近，Fomin 等人在这个方向上取得了进展，他们证明了该问题在每一类有向图上都是 FPT，而在这些有向图上，该问题都可以在多项式时间内求解。我们弱化了这一假设，从而改进了他们的结果：我们证明只需要一个多项式时间算法。

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

Information Processing Letters 工程技术-计算机：信息系统

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

7.3 months

期刊介绍： Information Processing Letters invites submission of original research articles that focus on fundamental aspects of information processing and computing. This naturally includes work in the broadly understood field of theoretical computer science; although papers in all areas of scientific inquiry will be given consideration, provided that they describe research contributions credibly motivated by applications to computing and involve rigorous methodology. High quality experimental papers that address topics of sufficiently broad interest may also be considered. Since its inception in 1971, Information Processing Letters has served as a forum for timely dissemination of short, concise and focused research contributions. Continuing with this tradition, and to expedite the reviewing process, manuscripts are generally limited in length to nine pages when they appear in print.