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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/14783

Title: Linear-Time Algorithm for Sliding Tokens on Trees
Authors: Demaine, Erik D.
Demaine, Martin L.
Fox-Epstein, Eli
Hoang, Duc A.
Ito, Takehiro
Ono, Hirotaka
Otachi, Yota
Uehara, Ryuhei
Yamada, Takeshi
Keywords: combinatorial reconfiguration
graph algorithm
independent set
sliding token
tree
Issue Date: 2015-07-28
Publisher: Elsevier
Magazine name: Theoretical Computer Science
Volume: 600
Start page: 132
End page: 142
DOI: 10.1016/j.tcs.2015.07.037
Abstract: Suppose that we are given two independent sets I_b and I_r of a graph such that |I_b| = |I_r|, and imagine that a token is placed on each vertex in I_b. Then, the sliding token problem is to determine whether there exists a sequence of independent sets which transforms I_b into I_r so that each independent set in the sequence results from the previous one by sliding exactly one token along an edge in the graph. This problem is known to be PSPACE-complete even for planar graphs, and also for bounded treewidth graphs. In this paper, we thus study the problem restricted to trees, and give the following three results: (1) the decision problem is solvable in linear time; (2) for a yes-instance, we can find in quadratic time an actual sequence of independent sets between I_b and I_r whose length (i.e., the number of token-slides) is quadratic; and (3) there exists an infinite family of instances on paths for which any sequence requires quadratic length.
Rights: Copyright (C)2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International license (CC BY-NC-ND 4.0). [http://creativecommons.org/licenses/by-nc-nd/4.0/] NOTICE: This is the author’s version of a work accepted for publication by Elsevier. Changes resulting from the publishing process, including peer review, editing, corrections, structural formatting and other quality control mechanisms, may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Erik D. Demaine, Martin L. Demaine, Eli Fox-Epstein, Duc A. Hoang, Takehiro Ito, Hirotaka Ono, Yota Otachi, Ryuhei Uehara, Takeshi Yamada, Theoretical Computer Science, 600, 2015, 132-142, http://dx.doi.org/10.1016/j.tcs.2015.07.037
URI: http://hdl.handle.net/10119/14783
Material Type: author
Appears in Collections:b10-1. 雑誌掲載論文 (Journal Articles)

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