Fixed-parameter tractability of token jumping on planar graphs

Takehiro Ito, Marcin Kamiński, Hirotaka Ono

Research output: Chapter in Book/Report/Conference proceedingChapter

13 Citations (Scopus)

Abstract

Suppose that we are given two independent sets I0 and Ir of a graph such that |I0| = |Ir|, and imagine that a token is placed on each vertex in I0. The token jumping problem is to determine whether there exists a sequence of independent sets of the same cardinality which transforms I0 into Ir so that each independent set in the sequence results from the previous one by moving exactly one token to another vertex. This problem is known to be PSPACE-complete even for planar graphs of maximum degree three, and W[1]-hard for general graphs when parameterized by the number of tokens. In this paper, we present a fixedparameter algorithm for token jumping on planar graphs, where the parameter is only the number of tokens. Furthermore, the algorithm can be modified so that it finds a shortest sequence for a yes-instance. The same scheme of the algorithms can be applied to a wider class of graphs which forbid a complete bipartite graph K3,t as a subgraph for a fixed integer t ≥ 3.

Original languageEnglish
Title of host publicationAlgorithms and Computation - 25th International Symposium, ISAAC 2014, Proceedings
EditorsHee-Kap Ahn, Chan-Su Shin
PublisherSpringer Verlag
Pages208-219
Number of pages12
ISBN (Electronic)9783319130743
DOIs
Publication statusPublished - Jan 1 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8889
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

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All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Ito, T., Kamiński, M., & Ono, H. (2014). Fixed-parameter tractability of token jumping on planar graphs. In H-K. Ahn, & C-S. Shin (Eds.), Algorithms and Computation - 25th International Symposium, ISAAC 2014, Proceedings (pp. 208-219). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8889). Springer Verlag. https://doi.org/10.1007/978-3-319-13075-0_17