Polynomial-Time Algorithm for Sliding Tokens on Trees
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.
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
Journal
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- Lecture Notes in Computer Science
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Lecture Notes in Computer Science 8889 389-400, 2014-12-15
Springer
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Details 詳細情報について
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- CRID
- 1050001337538492160
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- NII Article ID
- 120005850324
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- ISSN
- 03029743
- 16113349
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- Text Lang
- en
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- Article Type
- journal article
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- Data Source
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- IRDB
- Crossref
- CiNii Articles
- KAKEN