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Counting Temporal Paths

Authors Jessica Enright, Kitty Meeks , Hendrik Molter

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Author Details

Jessica Enright
  • School of Computing Science, University of Glasgow, UK
Kitty Meeks
  • School of Computing Science, University of Glasgow, UK
Hendrik Molter
  • Department of Computer Science and Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer-Sheva, Israel

Funding

  • Enright, Jessica: Supported by EPSRC grant EP/T004878/1.
  • Meeks, Kitty: Supported by EPSRC grants EP/T004878/1 and EP/V032305/1.
  • Molter, Hendrik: Supported by the ISF, grants No. 1456/18 and No. 1070/20, and European Research Council, grant number 949707.

Acknowledgements

This work was initiated at the Dagstuhl Seminar "Temporal Graphs: Structure, Algorithms, Applications" (Dagstuhl Seminar Nr. 21171).

Cite AsGet BibTex

Jessica Enright, Kitty Meeks, and Hendrik Molter. Counting Temporal Paths. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 30:1-30:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.STACS.2023.30

Abstract

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.

Subject Classification

ACM Subject Classification
  • 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
Keywords
  • Temporal Paths
  • Temporal Graphs
  • Parameterised Counting
  • Approximate Counting
  • #P-hard Counting Problems
  • Temporal Betweenness Centrality

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