Polynomial-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: Chapter

14 被引用数 (Scopus)


Suppose that we are given two independent sets I b and Ir of a graph such that |Ib| = | Ir|, and imagine that a token is placed on each vertex in I b. Then, the sliding token problem is to determine whether there exists a sequence of independent sets which transforms Ib and I r 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.

ホスト出版物のタイトルAlgorithms and Computation - 25th International Symposium, ISAAC 2014, Proceedings
編集者Hee-Kap Ahn, Chan-Su Shin
出版社Springer Verlag
出版ステータスPublished - 2014


名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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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