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DOI: 10.4230/LIPIcs.ISAAC.2016.37

Sliding Tokens on a Cactus

Authors: Duc A. Hoang and Ryuhei Uehara

Published in: LIPIcs, Volume 64, 27th International Symposium on Algorithms and Computation (ISAAC 2016)

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.

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Duc A. Hoang and Ryuhei Uehara. Sliding Tokens on a Cactus. In 27th International Symposium on Algorithms and Computation (ISAAC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 64, pp. 37:1-37:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{hoang_et_al:LIPIcs.ISAAC.2016.37,
  author =	{Hoang, Duc A. and Uehara, Ryuhei},
  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 =	{Hong, Seok-Hee},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2016.37},
  URN =		{urn:nbn:de:0030-drops-68074},
  doi =		{10.4230/LIPIcs.ISAAC.2016.37},
  annote =	{Keywords: reconfiguration problem, token sliding, independent set, cactus}
}

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Sliding Tokens on a Cactus

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