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Novel Complexity Results for Temporal Separators with Deadlines

Authors Riccardo Dondi , Manuel Lafond

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LIPIcs.WADS.2025.23.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Theory of computation → Graph algorithms analysis
  • Mathematics of computing → Graph theory
Keywords
  • Temporal Graphs
  • Graph Algorithms
  • Graph Separators
  • Parameterized Complexity
  • Approximation Complexity

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Abstract

We consider two variants, (s,z,𝓁)-Temporal Separator and (s,z,𝓁)-Temporal Cut, respectively, of the vertex separator and the edge cut problem in temporal graphs. The goal is to remove the minimum number of vertices (temporal edges, respectively) in order to delete all the temporal paths that have time travel at most 𝓁 between a source vertex s and target vertex z. First, we solve an open problem in the literature showing that (s,z,𝓁)-Temporal Separator is NP-hard even when the underlying graph has pathwidth bounded by four. We complement this result showing that (s,z,𝓁)-Temporal Separator can be solved in polynomial time for graphs of pathwidth bounded by three. Then we consider the approximability of (s,z,𝓁)-Temporal Separator and we show that it cannot be approximated within factor 2^Ω(log^{1-ε}|V|) for any constant ε > 0, unless NP ⊆ ZPP (V is the vertex set of the input temporal graph) and that the strict version is approximable within factor 𝓁-1 (we show also that it is unliklely that this factor can be improved). Then we consider the (s,z,𝓁)-Temporal Cut problem, we show that it is APX-hard and we present a 2 log₂(2𝓁) approximation algorithm.

Cite As Get BibTex

Riccardo Dondi and Manuel Lafond. Novel Complexity Results for Temporal Separators with Deadlines. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 23:1-23:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.WADS.2025.23

Author Details

Riccardo Dondi
  • Università degli Studi di Bergamo, Italy
Manuel Lafond
  • Université de Sherbrooke, Canada

References

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