eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-03-03
30:1
30:19
10.4230/LIPIcs.STACS.2023.30
article
Counting Temporal Paths
Enright, Jessica
1
Meeks, Kitty
1
https://orcid.org/0000-0001-5299-3073
Molter, Hendrik
2
https://orcid.org/0000-0002-4590-798X
School of Computing Science, University of Glasgow, UK
Department of Computer Science and Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer-Sheva, Israel
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol254-stacs2023/LIPIcs.STACS.2023.30/LIPIcs.STACS.2023.30.pdf
Temporal Paths
Temporal Graphs
Parameterised Counting
Approximate Counting
#P-hard Counting Problems
Temporal Betweenness Centrality