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Half-Space Separation in Monophonic Convexity

Authors Mohammed Elaroussi , Lhouari Nourine , Simon Vilmin

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ACM Subject Classification
  • Mathematics of computing → Paths and connectivity problems
  • Mathematics of computing → Graph algorithms
Keywords
  • chordless paths
  • monophonic convexity
  • separation
  • half-space

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Abstract

We study half-space separation in the convexity of chordless paths of a graph, i.e., monophonic convexity. In this problem, one is given a graph and two (disjoint) subsets of vertices and asks whether these two sets can be separated by complementary convex sets, called half-spaces. While it is known this problem is NP-complete for geodesic convexity - the convexity of shortest paths - we show that it can be solved in polynomial time for monophonic convexity.

Cite As Get BibTex

Mohammed Elaroussi, Lhouari Nourine, and Simon Vilmin. Half-Space Separation in Monophonic Convexity. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 51:1-51:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.MFCS.2024.51

Author Details

Mohammed Elaroussi
  • Université de Bejaia, Faculté des Sciences Exactes, Unité de Recherche LaMOS, 06000 Bejaia, Algeria
Lhouari Nourine
  • Université Clermont-Auvergne, CNRS, Mines de Saint-Étienne, Clermont-Auvergne-INP, LIMOS, 63000 Clermont-Ferrand, France
Simon Vilmin
  • Aix-Marseille Université, CNRS, LIS, Marseille, France

Funding

The first two authors have been funded by the CMEP Tassili project: "Argumentation et jeux: Structures et Algorithmes", Codes: 46085QH-21MDU320 PHC, 2021-2023. This research is also supported by the French government IDEXISITE initiative 16-IDEX-0001 (CAP 20-25).

Acknowledgements

We thank the reviewers for their comments. We are also grateful to Victor Chepoi for suggesting the term "shadow" instead of "extension" as well as pointing us to further references, especially the recent works on monophonic convexity [Bressan et al., 2024; Chepoi, 2024].

References

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