Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Komusiewicz, Christian; Morawietz, Nils https://www.dagstuhl.de/lipics License: Creative Commons Attribution 4.0 license (CC BY 4.0)
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URN: urn:nbn:de:0030-drops-168644
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Finding 3-Swap-Optimal Independent Sets and Dominating Sets Is Hard

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Abstract

For PLS-complete local search problems, there is presumably no polynomial-time algorithm which finds a locally optimal solution, even though determining whether a solution is locally optimal and replacing it by a better one if this is not the case can be done in polynomial time.
We study local search for Weighted Independent Set and Weighted Dominating Set with the 3-swap neighborhood. The 3-swap neighborhood of a vertex set S in G is the set of vertex sets which can be obtained from S by exchanging at most three vertices. We prove the following dichotomy: On the negative side, the problem of finding a 3-swap-optimal independent set or dominating set is PLS-complete. On the positive side, locally optimal independent sets or dominating sets can be found in polynomial time when allowing all 3-swaps except a) the swaps that remove two vertices from the current solution and add one vertex to the solution or b) the swaps that remove one vertex from the current solution and add two vertices to the solution.

BibTeX - Entry

@InProceedings{komusiewicz_et_al:LIPIcs.MFCS.2022.66,
  author =	{Komusiewicz, Christian and Morawietz, Nils},
  title =	{{Finding 3-Swap-Optimal Independent Sets and Dominating Sets Is Hard}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{66:1--66:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16864},
  URN =		{urn:nbn:de:0030-drops-168644},
  doi =		{10.4230/LIPIcs.MFCS.2022.66},
  annote =	{Keywords: Local Search, Graph problems, 3-swap neighborhood, PLS-completeness}
}

Keywords: Local Search, Graph problems, 3-swap neighborhood, PLS-completeness
Seminar: 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)
Issue date: 2022
Date of publication: 22.08.2022


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