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.ISAAC.2016.37
URN: urn:nbn:de:0030-drops-68074
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6807/
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Hoang, Duc A. ; Uehara, Ryuhei

Sliding Tokens on a Cactus

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LIPIcs-ISAAC-2016-37.pdf (0.7 MB)

Abstract

Given two independent sets I and J of a graph G, imagine that a token (coin) is placed on each vertex in I. Then, the Sliding Token problem asks if one could transforms I to J using a sequence of elementary steps, where each step requires sliding a token from one vertex to one of its neighbors, such that the resulting set of vertices where tokens are placed still remains independent. In this paper, we describe a polynomial-time algorithm for solving Sliding Token in case the graph G is a cactus. Our algorithm is designed based on two observations. First, all structures that forbid the existence of a sequence of token slidings between I and J, if exist, can be found in polynomial time. A no-instance may be easily deduced using this characterization. Second, without such forbidden structures, a sequence of token slidings between I and J does exist.

BibTeX - Entry

@InProceedings{hoang_et_al:LIPIcs:2016:6807,
  author =	{Duc A. Hoang and Ryuhei Uehara},
  title =	{{Sliding Tokens on a Cactus}},
  booktitle =	{27th International Symposium on Algorithms and Computation (ISAAC 2016)},
  pages =	{37:1--37:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-026-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{64},
  editor =	{Seok-Hee Hong},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6807},
  URN =		{urn:nbn:de:0030-drops-68074},
  doi =		{10.4230/LIPIcs.ISAAC.2016.37},
  annote =	{Keywords: reconfiguration problem, token sliding, independent set, cactus}
}

Keywords: reconfiguration problem, token sliding, independent set, cactus
Collection: 27th International Symposium on Algorithms and Computation (ISAAC 2016)
Issue Date: 2016
Date of publication: 07.12.2016

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