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DOI: 10.4230/LIPIcs.MFCS.2024.51

Half-Space Separation in Monophonic Convexity

Authors: Mohammed Elaroussi, Lhouari Nourine, and Simon Vilmin

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

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.

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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)

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@InProceedings{elaroussi_et_al:LIPIcs.MFCS.2024.51,
  author =	{Elaroussi, Mohammed and Nourine, Lhouari and Vilmin, Simon},
  title =	{{Half-Space Separation in Monophonic Convexity}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{51:1--51:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.51},
  URN =		{urn:nbn:de:0030-drops-206070},
  doi =		{10.4230/LIPIcs.MFCS.2024.51},
  annote =	{Keywords: chordless paths, monophonic convexity, separation, half-space}
}

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Half-Space Separation in Monophonic Convexity

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