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Distance to Transitivity: New Parameters for Taming Reachability in Temporal Graphs

Authors Arnaud Casteigts , Nils Morawietz , Petra Wolf

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Author Details

Arnaud Casteigts
  • Department of Computer Science, University of Geneva, Switzerland
Nils Morawietz
  • Institute of Computer Science, Friedrich Schiller University Jena, Germany
Petra Wolf
  • LaBRI, CNRS, Université de Bordeaux, Bordeaux INP, France

Funding

  • Casteigts, Arnaud: supported by French ANR, project ANR-22-CE48-0001 (TEMPOGRAL).
  • Wolf, Petra: supported by French ANR, project ANR-22-CE48-0001 (TEMPOGRAL).

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Arnaud Casteigts, Nils Morawietz, and Petra Wolf. Distance to Transitivity: New Parameters for Taming Reachability in Temporal Graphs. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 36:1-36:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.MFCS.2024.36

Abstract

A temporal graph is a graph whose edges only appear at certain points in time. Reachability in these graphs is defined in terms of paths that traverse the edges in chronological order (temporal paths). This form of reachability is neither symmetric nor transitive, the latter having important consequences on the computational complexity of even basic questions, such as computing temporal connected components. In this paper, we introduce several parameters that capture how far a temporal graph 𝒢 is from being transitive, namely, vertex-deletion distance to transitivity and arc-modification distance to transitivity, both being applied to the reachability graph of 𝒢. We illustrate the impact of these parameters on the temporal connected component problem, obtaining several tractability results in terms of fixed-parameter tractability and polynomial kernels. Significantly, these results are obtained without restrictions of the underlying graph, the snapshots, or the lifetime of the input graph. As such, our results isolate the impact of non-transitivity and confirm the key role that it plays in the hardness of temporal graph problems.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Mathematics of computing → Discrete mathematics
Keywords
  • Temporal graphs
  • Parameterized complexity
  • Reachability
  • Transitivity

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