License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2023.30
URN: urn:nbn:de:0030-drops-176829
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17682/
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Enright, Jessica ; Meeks, Kitty ; Molter, Hendrik

Counting Temporal Paths

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LIPIcs-STACS-2023-30.pdf (0.8 MB)

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.

BibTeX - Entry

@InProceedings{enright_et_al:LIPIcs.STACS.2023.30,
  author =	{Enright, Jessica and Meeks, Kitty and Molter, Hendrik},
  title =	{{Counting Temporal Paths}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{30:1--30:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/17682},
  URN =		{urn:nbn:de:0030-drops-176829},
  doi =		{10.4230/LIPIcs.STACS.2023.30},
  annote =	{Keywords: Temporal Paths, Temporal Graphs, Parameterised Counting, Approximate Counting, #P-hard Counting Problems, Temporal Betweenness Centrality}
}

Keywords: Temporal Paths, Temporal Graphs, Parameterised Counting, Approximate Counting, #P-hard Counting Problems, Temporal Betweenness Centrality
Collection: 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)
Issue Date: 2023
Date of publication: 03.03.2023

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