Making the interval membership width of temporal graphs connected and bidirectional

IF 1.1 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences Pub Date : 2025-07-03 DOI:10.1016/j.jcss.2025.103684

Filippos Christodoulou , Pierluigi Crescenzi , Andrea Marino , Ana Silva , Dimitrios M. Thilikos

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引用次数: 0

Abstract

Temporal graphs are graphs that evolve over time. Many problems which are polynomial-time solvable in standard graphs become NP-hard when appropriately defined in the realm of temporal graphs.This suggested the definition of several parameters for temporal graphs and to prove the fixed-parameter tractability of several problems with respect to these parameters. In this paper, we introduce a hierarchy of parameters based on the previously defined interval membership width and the temporal evolution of the connected components of the underlying static graph. We show that the Eulerian trail problem and the temporal 2-coloring problem are both fixed-parameter tractable with respect to any parameter in the hierarchy. We also introduce a vertex-variant of the parameters and show that the firefighter problem, known to be FPT with respect to the vertex-variant of the interval membership width, is also FPT with respect to one of the parameters in the second level of the hierarchy.

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使时间图的区间隶属度宽度连通和双向

时间图是随时间变化的图。许多在标准图中多项式时间可解的问题，在时间图中适当地定义后，就变成了np困难问题。提出了时间图的几个参数的定义，并证明了几个问题相对于这些参数的定参数可跟踪性。在本文中，我们引入了一个基于先前定义的区间隶属度宽度和底层静态图的连通分量的时间演化的参数层次结构。我们证明了欧拉轨迹问题和时间2-着色问题对于层次结构中的任何参数都是固定参数可处理的。我们还引入了参数的一个顶点变量，并表明消防员问题，已知是相对于区间隶属度宽度的顶点变量的FPT，也是相对于层次结构第二层中的一个参数的FPT。

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 工程技术-计算机：理论方法

CiteScore

3.70

自引率

0.00%

发文量

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.