Parameterized temporal exploration problems

Erlebach, Thomas; Spooner, Jakob T.

Abstract

In this paper we study the fixed-parameter tractability of the problem of deciding whether a given temporal graph G admits a temporal walk that visits all vertices (temporal exploration) or, in some problem variants, a certain subset of the vertices. Formally, a temporal graph is a sequence G = hG1, . . . , GLi of graphs with V (Gt) = V (G) and E(Gt) ⊆ E(G) for all t ∈ [L] and some underlying graph G, and a temporal walk is a timerespecting sequence of edge-traversals. We consider both the strict variant, in which edges must be traversed in strictly increasing timesteps, and the non-strict variant, in which an arbitrary number of edges can be traversed in each timestep. For both variants, we give FPT algorithms for the problem of finding a temporal walk that visits a given set X of vertices, parameterized by |X|, and for the problem of finding a temporal walk that visits at least k distinct vertices in V (G), parameterized by k. We also show W[2]-hardness for a set version of the temporal exploration problem for both variants. For the non-strict variant, we give an FPT algorithm for the temporal exploration problem parameterized by the lifetime of the input graph, and we show that the temporal exploration problem can be solved in polynomial time if the graph in each timestep has at most two connected components.

Citation

Erlebach, T., & Spooner, J. T. (2023). Parameterized temporal exploration problems. Journal of Computer and System Sciences, 135, 73-88. https://doi.org/10.1016/j.jcss.2023.01.003

• Journal Article Type: Article
• Acceptance Date: Jan 19, 2023
• Online Publication Date: Mar 6, 2023
• Publication Date: 2023
• Deposit Date: Jan 23, 2023
• Publicly Available Date: Jan 30, 2023
• Journal: Journal of Computer and System Sciences
• Print ISSN: 0022-0000
• Electronic ISSN: 1090-2724
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 135
• Pages: 73-88
• DOI: https://doi.org/10.1016/j.jcss.2023.01.003
• Public URL: https://durham-repository.worktribe.com/output/1184842