An FPT algorithm for timeline cover

IF 1.1 3区 计算机科学 Q1 BUSINESS, FINANCE
Riccardo Dondi , Manuel Lafond
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引用次数: 0

Abstract

One of the most studied problem in theoretical computer science, Vertex Cover, has been recently considered in the temporal graph framework. Here we study a Vertex Cover variant, called k-TimelineCover. Given a temporal graph k-TimelineCover asks to define an interval for each vertex so that for every temporal edge existing in a timestamp t, at least one of the endpoints has an interval that includes t. The goal is to decide whether it is possible to cover every temporal edge while using vertex intervals of total span at most k. k-TimelineCover has been shown to be NP-hard, but its parameterized complexity has not been fully understood when parameterizing by the span of the solution. We settle this open problem by giving an FPT algorithm that combines two techniques, a modified form of iterative compression and a reduction to Digraph Pair Cut.
时间线覆盖的FPT算法
顶点覆盖是理论计算机科学中研究最多的问题之一,最近在时间图框架中得到了考虑。这里我们研究一个顶点覆盖的变体,称为k-TimelineCover。给定一个时序图k-TimelineCover要求为每个顶点定义一个间隔,这样每时间边缘存在一个时间戳t,至少有一个端点的一个区间,其中包括t。我们的目标是决定是否可以覆盖每一个时间边缘在使用顶点总跨度的间隔最多k k-TimelineCover已被证明是np困难,但其参数化的复杂性尚未完全理解当张成的空间参数化的解决方案。我们给出了一种FPT算法,该算法结合了两种技术,一种改进的迭代压缩形式和对有向图对切割的简化。
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
Journal of Computer and System Sciences
Journal of Computer and System Sciences 工程技术-计算机:理论方法
CiteScore
3.70
自引率
0.00%
发文量
58
审稿时长
68 days
期刊介绍: The Journal of Computer and System Sciences publishes original research papers in computer science and related subjects in system science, with attention to the relevant mathematical theory. Applications-oriented papers may also be accepted and they are expected to contain deep analytic evaluation of the proposed solutions. Research areas include traditional subjects such as: • Theory of algorithms and computability • Formal languages • Automata theory Contemporary subjects such as: • Complexity theory • Algorithmic Complexity • Parallel & distributed computing • Computer networks • Neural networks • Computational learning theory • Database theory & practice • Computer modeling of complex systems • Security and Privacy.
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