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

33 Citations (Scopus)


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
Number of pages11
ISBN (Print)9783319060880
Publication statusPublished - 2014
Event11th Annual Conference on Theory and Applications of Models of Computation, TAMC 2014 - Chennai, India
Duration: Apr 11 2014Apr 13 2014

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


Other11th Annual Conference on Theory and Applications of Models of Computation, TAMC 2014

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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