Counting Temporal Paths

Enright, J. , Meeks, K. and Molter, H. (2023) Counting Temporal Paths. In: 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023), Hamburg, Germany, 07-10 Mar 2023, p. 30. (doi: 10.4230/LIPIcs.STACS.2023.30)

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The betweenness centrality of a vertex v is an important centrality measure that quantifies how many optimal paths between pairs of other vertices visit v. Computing betweenness centrality in a temporal graph, in which the edge set may change over discrete timesteps, requires us to count temporal paths that are optimal with respect to some criterion. For several natural notions of optimality, including foremost or fastest temporal paths, this counting problem reduces to #TEMPORAL PATH, the problem of counting all temporal paths between a fixed pair of vertices; like the problems of counting foremost and fastest temporal paths, #TEMPORAL PATH is #P-hard in general. Motivated by the many applications of this intractable problem, we initiate a systematic study of the parameterised and approximation complexity of #TEMPORAL PATH. We show that the problem presumably does not admit an FPT-algorithm for the feedback vertex number of the static underlying graph, and that it is hard to approximate in general. On the positive side, we prove several exact and approximate FPT-algorithms for special cases.

Item Type:Conference Proceedings
Glasgow Author(s) Enlighten ID:Enright, Dr Jessica and Meeks, Dr Kitty
Authors: Enright, J., Meeks, K., and Molter, H.
College/School:College of Science and Engineering > School of Computing Science
Copyright Holders:Copyright © 2023 Jessica Enright, Kitty Meeks, and Hendrik Molter
First Published:First published in Proceedings of the 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023): 30
Publisher Policy:Reproduced under a Creative Commons License
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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
305944Multilayer Algorithmics to Leverage Graph StructureKitty MeeksEngineering and Physical Sciences Research Council (EPSRC)EP/T004878/1M&S - Statistics
312197Beyond One Solution in Combinatorial OptimisationKitty MeeksEngineering and Physical Sciences Research Council (EPSRC)EP/V032305/1Computing Science