License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2019.12
URN: urn:nbn:de:0030-drops-109568
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10956/
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Konstantinidis, Athanasios L. ; Papadopoulos, Charis

Cluster Deletion on Interval Graphs and Split Related Graphs

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LIPIcs-MFCS-2019-12.pdf (0.7 MB)

Abstract

In the Cluster Deletion problem the goal is to remove the minimum number of edges of a given graph, such that every connected component of the resulting graph constitutes a clique. It is known that the decision version of Cluster Deletion is NP-complete on (P_5-free) chordal graphs, whereas Cluster Deletion is solved in polynomial time on split graphs. However, the existence of a polynomial-time algorithm of Cluster Deletion on interval graphs, a proper subclass of chordal graphs, remained a well-known open problem. Our main contribution is that we settle this problem in the affirmative, by providing a polynomial-time algorithm for Cluster Deletion on interval graphs. Moreover, despite the simple formulation of the algorithm on split graphs, we show that Cluster Deletion remains NP-complete on a natural and slight generalization of split graphs that constitutes a proper subclass of P_5-free chordal graphs. Although the later result arises from the already-known reduction for P_5-free chordal graphs, we give an alternative proof showing an interesting connection between edge-weighted and vertex-weighted variations of the problem. To complement our results, we provide faster and simpler polynomial-time algorithms for Cluster Deletion on subclasses of such a generalization of split graphs.

BibTeX - Entry

@InProceedings{konstantinidis_et_al:LIPIcs:2019:10956,
  author =	{Athanasios L. Konstantinidis and Charis Papadopoulos},
  title =	{{Cluster Deletion on Interval Graphs and Split Related Graphs}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{12:1--12:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Peter Rossmanith and Pinar Heggernes and Joost-Pieter Katoen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10956},
  URN =		{urn:nbn:de:0030-drops-109568},
  doi =		{10.4230/LIPIcs.MFCS.2019.12},
  annote =	{Keywords: Cluster deletion, interval graphs, split graphs}
}

Keywords: Cluster deletion, interval graphs, split graphs
Collection: 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)
Issue Date: 2019
Date of publication: 20.08.2019

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