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http://hdl.handle.net/10119/13765
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| 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
tree
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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