The parameterised complexity of generalised temporal domination on temporal graphs with modular structure

2026-09-22

AI Summary

本文研究了(α,β)-Temporal Dominating Set问题在具有模块化结构的时间图上的参数复杂性，使用时间邻域多样性、时间模块宽度和时间团宽等参数进行分析。

Abstract

Inspired by the static problem $(α,β)$-Dominating Set, we propose a general temporal domination problem, called $(α,β)$-Temporal Dominating Set ($(α,β)$-TDS). We show that this problem encompasses Temporal Dominating Set, and additionally provides first temporal extensions of problems such as $k$-Dominating Set and $α$-Dominating Set. In this paper, we study the parameterised complexity of $(α,β)$-TDS with respect to temporal neighbourhood diversity (TND), temporal modular-width (TMW), and temporal cliquewidth (TCW). We obtain fixed parameter tractability results for all values of $α$ and $β$ with respect to TND; W[1]-hardness with respect to TMW and TCW whenever $β$ is in the problem input, or whenever $α\in (0,1)$ and $β$ is a fixed constant; and para-NP-hardness with respect to TCW when $α= 0$ and $β= 1$, or $α= 1$ and $β= 0$.

Problem

• temporal domination
• parameterised complexity
• modular structure
• temporal graphs
• dominating set

Innovation

• Temporal Dominating Set
• Parameterised Complexity
• Temporal Neighborhood Diversity
• Temporal Modular-width
• Temporal Cliquewidth