Linear-time algorithm for sliding tokens on trees

Erik D. Demaine, Martin L. Demaine, Eli Fox-Epstein, Duc A. Hoang, Takehiro Ito, Hirotaka Ono, Yota Otachi, Ryuhei Uehara, Takeshi Yamada

研究成果: Article査読

33 被引用数 (Scopus)

抄録

Suppose that we are given two independent sets Ib and Ir of a 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 thus study the problem restricted to trees, and give the following three results: (1) the decision problem is solvable in linear time; (2) for a yes-instance, we can find in quadratic time an actual sequence of independent sets between Ib and Ir whose length (i.e., the number of token-slides) is quadratic; and (3) there exists an infinite family of instances on paths for which any sequence requires quadratic length.

本文言語English
ページ(範囲)132-142
ページ数11
ジャーナルTheoretical Computer Science
600
DOI
出版ステータスPublished - 2015 10 4

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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