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DOI: 10.4230/LIPIcs.FSTTCS.2016.34
URN: urn:nbn:de:0030-drops-68694
URL: http://drops.dagstuhl.de/opus/volltexte/2016/6869/
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de Berg, Mark ; Jansen, Bart M. P. ; Mukherjee, Debankur

Independent-Set Reconfiguration Thresholds of Hereditary Graph Classes

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Abstract

Traditionally, reconfiguration problems ask the question whether a given solution of an optimization problem can be transformed to a target solution in a sequence of small steps that preserve feasibility of the intermediate solutions. In this paper, rather than asking this question from an algorithmic perspective, we analyze the combinatorial structure behind it. We consider the problem of reconfiguring one independent set into another, using two different processes: (1) exchanging exactly k vertices in each step, or (2) removing or adding one vertex in each step while ensuring the intermediate sets contain at most k fewer vertices than the initial solution. We are interested in determining the minimum value of k for which this reconfiguration is possible, and bound these threshold values in terms of several structural graph parameters. For hereditary graph classes we identify structures that cause the reconfiguration threshold to be large.

BibTeX - Entry

@InProceedings{deberg_et_al:LIPIcs:2016:6869,
  author =	{Mark de Berg and Bart M. P. Jansen and Debankur Mukherjee},
  title =	{{Independent-Set Reconfiguration Thresholds of Hereditary Graph Classes}},
  booktitle =	{36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)},
  pages =	{34:1--34:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-027-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{65},
  editor =	{Akash Lal and S. Akshay and Saket Saurabh and Sandeep Sen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6869},
  URN =		{urn:nbn:de:0030-drops-68694},
  doi =		{10.4230/LIPIcs.FSTTCS.2016.34},
  annote =	{Keywords: Reconfiguration, Independent set, Token Addition Removal, Token Sliding}
}

Keywords: Reconfiguration, Independent set, Token Addition Removal, Token Sliding
Seminar: 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)
Issue Date: 2016
Date of publication: 08.12.2016


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