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DOI: 10.4230/LIPIcs.ISAAC.2016.37
URN: urn:nbn:de:0030-drops-68074
URL: https://drops.dagstuhl.de/opus/volltexte/2016/6807/
Hoang, Duc A. ; Uehara, Ryuhei
Sliding Tokens on a Cactus
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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 | |
| Seminar: | 27th International Symposium on Algorithms and Computation (ISAAC 2016) | |
| Issue date: | 2016 | |
| Date of publication: | 07.12.2016 |
