### Abstract

Suppose that we are given two independent sets I_{0} and I _{r} of a graph such that |I_{0}| = |I_{r}|, and imagine that a token is placed on each vertex in I_{0}. Then, the token jumping problem is to determine whether there exists a sequence of independent sets which transforms I_{0} into I_{r} 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 I_{0} and I_{r} with the minimum number of token movements.

Original language | English |
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Title of host publication | Theory and Applications of Models of Computation - 11th Annual Conference, TAMC 2014, Proceedings |

Publisher | Springer Verlag |

Pages | 341-351 |

Number of pages | 11 |

ISBN (Print) | 9783319060880 |

DOIs | |

Publication status | Published - Jan 1 2014 |

Event | 11th Annual Conference on Theory and Applications of Models of Computation, TAMC 2014 - Chennai, India Duration: Apr 11 2014 → Apr 13 2014 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 8402 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 11th Annual Conference on Theory and Applications of Models of Computation, TAMC 2014 |
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Country | India |

City | Chennai |

Period | 4/11/14 → 4/13/14 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*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

**On the parameterized complexity for token jumping on graphs.** / Ito, Takehiro; Kamiński, Marcin; Ono, Hirotaka; Suzuki, Akira; Uehara, Ryuhei; Yamanaka, Katsuhisa.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Theory and Applications of Models of Computation - 11th Annual Conference, TAMC 2014, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8402 LNCS, Springer Verlag, pp. 341-351, 11th Annual Conference on Theory and Applications of Models of Computation, TAMC 2014, Chennai, India, 4/11/14. https://doi.org/10.1007/978-3-319-06089-7_24

}

TY - GEN

T1 - On the parameterized complexity for token jumping on graphs

AU - Ito, Takehiro

AU - Kamiński, Marcin

AU - Ono, Hirotaka

AU - Suzuki, Akira

AU - Uehara, Ryuhei

AU - Yamanaka, Katsuhisa

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84958541436&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84958541436&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-06089-7_24

DO - 10.1007/978-3-319-06089-7_24

M3 - Conference contribution

AN - SCOPUS:84958541436

SN - 9783319060880

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 341

EP - 351

BT - Theory and Applications of Models of Computation - 11th Annual Conference, TAMC 2014, Proceedings

PB - Springer Verlag

ER -