On the parameterized complexity for token jumping on graphs

Takehiro Ito, Marcin Kamiński, Hirotaka Ono, Akira Suzuki, Ryuhei Uehara, Katsuhisa Yamanaka

Research output: Chapter in Book/Report/Conference proceedingConference contribution

22 Citations (Scopus)

Abstract

Suppose that we are given two independent sets I0 and I r of a graph such that |I0| = |Ir|, and imagine that a token is placed on each vertex in I0. Then, the token jumping problem is to determine whether there exists a sequence of independent sets 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. Therefore, all independent sets in the sequence must be of the same cardinality. This problem is PSPACE-complete even for planar graphs with maximum degree three. In this paper, we first show that the problem is W[1]-hard when parameterized only by the number of tokens. We then give an FPT algorithm for general graphs when parameterized by both the number of tokens and the maximum degree. Our FPT algorithm can be modified so that it finds an actual sequence of independent sets between I0 and Ir with the minimum number of token movements.

Original languageEnglish
Title of host publicationTheory and Applications of Models of Computation - 11th Annual Conference, TAMC 2014, Proceedings
PublisherSpringer-Verlag
Pages341-351
Number of pages11
ISBN (Print)9783319060880
DOIs
Publication statusPublished - 2014 Jan 1
Event11th Annual Conference on Theory and Applications of Models of Computation, TAMC 2014 - Chennai, India
Duration: 2014 Apr 112014 Apr 13

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8402 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other11th Annual Conference on Theory and Applications of Models of Computation, TAMC 2014
CountryIndia
CityChennai
Period14/4/1114/4/13

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Ito, T., Kamiński, M., Ono, H., Suzuki, A., Uehara, R., & Yamanaka, K. (2014). On the parameterized complexity for token jumping on graphs. In Theory and Applications of Models of Computation - 11th Annual Conference, TAMC 2014, Proceedings (pp. 341-351). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8402 LNCS). Springer-Verlag. https://doi.org/10.1007/978-3-319-06089-7_24