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Robust Temporal Cut

Authors Jessica Enright , Thomas Erlebach , Kitty Meeks , Nils Morawietz

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LIPIcs.SAND.2026.14.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • temporal graphs
  • minimum cut
  • parameterized complexity
  • FPT algorithms

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Abstract

In this paper we introduce the Robust Temporal Cut problem (RTC) defined as follows: For a given temporal graph with designated source node s and destination node z, and parameters δ and k, remove a minimum number of time edges so that, even if an adversary can adjust the time labels of up to k of the remaining time edges by adding or subtracting values bounded by δ, no temporal s-z path exists. We study the classical and parameterized complexity of RTC. In particular, we show for both strict and non-strict temporal paths that RTC is NP-complete for any combination of k ≥ 1 and δ ≥ 1 and W[1]-hard for parameter solution size or vertex interval membership width plus pathwidth of the underlying graph. Furthermore, we give approximation algorithms and FPT algorithms for parameters including temporal neighborhood diversity plus solution size, timed vertex cover size, and vertex cover size of the underlying graph plus solution size.

Cite As Get BibTex

Jessica Enright, Thomas Erlebach, Kitty Meeks, and Nils Morawietz. Robust Temporal Cut. In 5th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 373, pp. 14:1-14:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SAND.2026.14

Author Details

Jessica Enright
  • School of Computing Science, University of Glasgow, UK
Thomas Erlebach
  • Department of Computer Science, Durham University, UK
Kitty Meeks
  • School of Computing Science, University of Glasgow, UK
Nils Morawietz
  • LaBRI, Université de Bordeaux, Talence, France
  • Institute of Computer Science, Friedrich Schiller University Jena, Germany

Funding

  • Morawietz, Nils: Supported by the French ANR, project ANR-22-CE48-0001 (TEMPOGRAL).

Acknowledgements

The authors would like to thank David C. Kutner for helpful discussions regarding the design of an FPT algorithm with respect to temporal neighborhood diversity.

References

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