Polynomial-Time Algorithm for Sliding Tokens on Trees

• Demaine, Erik D.

• Demaine, Martin

• Fox-Epstein, Eli

• Hoang, Duc A.

• Ito, Takehiro

• Ono, Hirotaka

• Otachi, Yota

• Uehara, Ryuhei

• Yamada, Takeshi

抄録

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.

Algorithms and Computation, 25th International Symposium, ISAAC 2014, Jeonju, Korea, December 15-17, 2014, Proceedings

identifier:https://dspace.jaist.ac.jp/dspace/handle/10119/13765

収録刊行物

• Lecture Notes in Computer Science

  Lecture Notes in Computer Science 8889 389-400, 2014-12-15

  Springer

キーワード

• reconfiguration problem
• independent set
• tree
• token sliding

詳細情報

• CRID: 1050001337538492160
• NII論文ID: 120005850324
• ISSN: 03029743
• ISSN: 16113349
• DOI: 10.1007/978-3-319-13075-0_31
• Web Site: http://hdl.handle.net/10119/13765
• Web Site: http://link.springer.com/content/pdf/10.1007/978-3-319-13075-0_31
• 本文言語コード: en
• 資料種別: journal article
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