Counting Temporal Paths
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.
Temporal Paths
Temporal Graphs
Parameterised Counting
Approximate Counting
#P-hard Counting Problems
Temporal Betweenness Centrality
Theory of computation~Graph algorithms analysis
Theory of computation~Parameterized complexity and exact algorithms
Theory of computation~Approximation algorithms analysis
Mathematics of computing~Discrete mathematics
30:1-30:19
Regular Paper
https://arxiv.org/abs/2202.12055
This work was initiated at the Dagstuhl Seminar "Temporal Graphs: Structure, Algorithms, Applications" (Dagstuhl Seminar Nr. 21171).
Jessica
Enright
Jessica Enright
School of Computing Science, University of Glasgow, UK
Supported by EPSRC grant EP/T004878/1.
Kitty
Meeks
Kitty Meeks
School of Computing Science, University of Glasgow, UK
https://orcid.org/0000-0001-5299-3073
Supported by EPSRC grants EP/T004878/1 and EP/V032305/1.
Hendrik
Molter
Hendrik Molter
Department of Computer Science and Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer-Sheva, Israel
https://orcid.org/0000-0002-4590-798X
Supported by the ISF, grants No. 1456/18 and No. 1070/20, and European Research Council, grant number 949707.
10.4230/LIPIcs.STACS.2023.30
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Jessica Enright, Kitty Meeks, and Hendrik Molter
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