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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/16224

Title: Swapping Colored Tokens on Graphs
Authors: Yamanaka, Katsuhisa
Horiyama, Takashi
Keil, J. Mark
Kirkpatrick, David
Otachi, Yota
Saitoh, Toshiki
Uehara, Ryuhei
Uno, Yushi
Keywords: computational complexity
fixed-parameter algorithm
token swapping
colored token swapping
Issue Date: 2018-03-19
Publisher: Elsevier
Magazine name: Theoretical Computer Science
Volume: 729
Start page: 1
End page: 10
DOI: 10.1016/j.tcs.2018.03.016
Abstract: We investigate the computational complexity of the following problem. We are given a graph in which each vertex has an initial and a target color. Each pair of adjacent vertices can swap their current colors. Our goal is to perform the minimum number of swaps so that the current and targetcolors agree at each vertex. When the colors are chosen from {1, 2, ..., c}, we call this problem c-Colored Token Swapping since the current color of a vertex can be seen as a colored token placed on the vertex. We show that c-Colored Token Swapping is NP-complete for c=3 even if input graphs are restricted to connected planar bipartite graphs of maximum degree 3. We then show that 2-Colored Token Swapping can be solved in polynomial time for general graphs and in linear time for trees. Besides, we show that, the problem for complete graphs is fixed-parameter tractable when parameterized by the number of colors, while it is known to be NP-complete when the number of colors is unbounded.
Rights: Copyright (C)2018, 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. Katsuhisa Yamanaka, Takashi Horiyama, J. Mark Keil, David Kirkpatrick, Yota Otachi, Toshiki Saitoh, Ryuhei Uehara, Yushi Uno, Theoretical Computer Science, 729, 2018, 1-10, http://dx.doi.org/10.1016/j.tcs.2018.03.016
URI: http://hdl.handle.net/10119/16224
Material Type: author
Appears in Collections:b10-1. 雑誌掲載論文 (Journal Articles)

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