### Abstract

Suppose that we are given two dominating sets D
_{s}
and D
_{t}
of a graph G whose cardinalities are at most a given threshold k. Then, we are asked whether there exists a sequence of dominating sets of G between D
_{s}
and D
_{t}
such that each dominating set in the sequence is of cardinality at most k and can be obtained from the previous one by either adding or deleting exactly one vertex. This decision problem is known to be PSPACE-complete in general. In this paper, we study the complexity of this problem from the viewpoint of graph classes. We first prove that the problem remains PSPACE-complete even for planar graphs, bounded bandwidth graphs, split graphs, and bipartite graphs. We then give a general scheme to construct linear-time algorithms and show that the problem can be solved in linear time for cographs, forests, and interval graphs. Furthermore, for these tractable cases, we can obtain a desired sequence if it exists such that the number of additions and deletions is bounded by O(n), where n is the number of vertices in the input graph.

Original language | English |
---|---|

Pages (from-to) | 37-49 |

Number of pages | 13 |

Journal | Theoretical Computer Science |

Volume | 651 |

DOIs | |

Publication status | Published - Oct 25 2016 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Theoretical Computer Science*,

*651*, 37-49. https://doi.org/10.1016/j.tcs.2016.08.016

**The complexity of dominating set reconfiguration.** / Haddadan, Arash; Ito, Takehiro; Mouawad, Amer E.; Nishimura, Naomi; Ono, Hirotaka; Suzuki, Akira; Tebbal, Youcef.

Research output: Contribution to journal › Article

*Theoretical Computer Science*, vol. 651, pp. 37-49. https://doi.org/10.1016/j.tcs.2016.08.016

}

TY - JOUR

T1 - The complexity of dominating set reconfiguration

AU - Haddadan, Arash

AU - Ito, Takehiro

AU - Mouawad, Amer E.

AU - Nishimura, Naomi

AU - Ono, Hirotaka

AU - Suzuki, Akira

AU - Tebbal, Youcef

PY - 2016/10/25

Y1 - 2016/10/25

N2 - Suppose that we are given two dominating sets D s and D t of a graph G whose cardinalities are at most a given threshold k. Then, we are asked whether there exists a sequence of dominating sets of G between D s and D t such that each dominating set in the sequence is of cardinality at most k and can be obtained from the previous one by either adding or deleting exactly one vertex. This decision problem is known to be PSPACE-complete in general. In this paper, we study the complexity of this problem from the viewpoint of graph classes. We first prove that the problem remains PSPACE-complete even for planar graphs, bounded bandwidth graphs, split graphs, and bipartite graphs. We then give a general scheme to construct linear-time algorithms and show that the problem can be solved in linear time for cographs, forests, and interval graphs. Furthermore, for these tractable cases, we can obtain a desired sequence if it exists such that the number of additions and deletions is bounded by O(n), where n is the number of vertices in the input graph.

AB - Suppose that we are given two dominating sets D s and D t of a graph G whose cardinalities are at most a given threshold k. Then, we are asked whether there exists a sequence of dominating sets of G between D s and D t such that each dominating set in the sequence is of cardinality at most k and can be obtained from the previous one by either adding or deleting exactly one vertex. This decision problem is known to be PSPACE-complete in general. In this paper, we study the complexity of this problem from the viewpoint of graph classes. We first prove that the problem remains PSPACE-complete even for planar graphs, bounded bandwidth graphs, split graphs, and bipartite graphs. We then give a general scheme to construct linear-time algorithms and show that the problem can be solved in linear time for cographs, forests, and interval graphs. Furthermore, for these tractable cases, we can obtain a desired sequence if it exists such that the number of additions and deletions is bounded by O(n), where n is the number of vertices in the input graph.

UR - http://www.scopus.com/inward/record.url?scp=84991404907&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84991404907&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2016.08.016

DO - 10.1016/j.tcs.2016.08.016

M3 - Article

AN - SCOPUS:84991404907

VL - 651

SP - 37

EP - 49

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

ER -