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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/13765

Title: Polynomial-Time Algorithm for Sliding Tokens on Trees
Authors: Demaine, Erik D.
Demaine, Martin
Fox-Epstein, Eli
Hoang, Duc A.
Ito, Takehiro
Ono, Hirotaka
Otachi, Yota
Uehara, Ryuhei
Yamada, Takeshi
Keywords: reconfiguration problem
independent set
token sliding
Issue Date: 2014-12-15
Publisher: Springer
Magazine name: Lecture Notes in Computer Science
Volume: 8889
Start page: 389
End page: 400
DOI: 10.1007/978-3-319-13075-0_31
Abstract: Suppose that we are given two independent sets Ib and Ir ofa graph such that |Ib| = |Ir|, and imagine that a token is placed on each vertex in Ib. Then, the SLIDING TOKEN problem is to determine whether there exists a sequence of independent sets which transforms Ib into Ir 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 show that the problem is solvable for trees in quadratic time. Our proof is constructive: for a yes-instance, we can find an actual sequence of independent sets between Ib and Ir whose length (i.e., the number of token-slides) is quadratic. We note that there exists an infinite family of instances on paths for which any sequence requires quadratic length.
Rights: This is the author-created version of Springer, Erik D. Demaine, Martin Demaine, Eli Fox-Epstein, Duc A. Hoang, Takehiro Ito, Hirotaka Ono, Yota Otachi, Ryuhei Uehara and Takeshi Yamada, Lecture Notes in Computer Science, 8889, 2014, 389-400. The original publication is available at www.springerlink.com, http://dx.doi.org/10.1007/978-3-319-13075-0_31
URI: http://hdl.handle.net/10119/13765
Material Type: author
Appears in Collections:b10-1. 雑誌掲載論文 (Journal Articles)

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