Parameterised temporal exploration problems

We study the fixed-parameter tractability of the problem of deciding whether a given temporal graph admits a temporal walk that visits all vertices (temporal exploration) or, in some variants, a certain subset of the vertices. In the strict variant, edges must be traversed in strictly increasing tim...

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Bibliographic Details
Published in:Journal of computer and system sciences Vol. 135; pp. 73 - 88
Main Authors: Erlebach, Thomas, Spooner, Jakob T.
Format: Journal Article
Language:English
Published: Elsevier Inc 01.08.2023
Subjects:
Fixed-parameter tractability
Parameterised complexity
Temporal graphs
Temporal graphs
Fixed-parameter tractability
Parameterised complexity
ISSN:0022-0000, 1090-2724
Online Access:Get full text
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Summary:We study the fixed-parameter tractability of the problem of deciding whether a given temporal graph admits a temporal walk that visits all vertices (temporal exploration) or, in some variants, a certain subset of the vertices. In the strict variant, edges must be traversed in strictly increasing timesteps; in the non-strict variant, any number of edges can be traversed in each timestep. For both variants, we give FPT algorithms for finding a temporal walk that visits a given set X of vertices, parameterised by |X|, and for finding a temporal walk that visits at least k distinct vertices, parameterised by k. We also show W[2]-hardness for a set version of temporal exploration. For the non-strict variant, we give an FPT algorithm for temporal exploration parameterised by the lifetime, and show that temporal exploration can be solved in polynomial time if the graph in each timestep has at most two connected components.
ISSN:0022-0000
1090-2724
DOI:10.1016/j.jcss.2023.01.003