The complexity of dominating set reconfiguration

Arash Haddadan, Takehiro Ito, Amer E. Mouawad, Naomi Nishimura, Hirotaka Ono, Akira Suzuki, Youcef Tebbal

Research output: Contribution to journalArticle

9 Citations (Scopus)

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 languageEnglish
Pages (from-to)37-49
Number of pages13
JournalTheoretical Computer Science
Volume651
DOIs
Publication statusPublished - Oct 25 2016

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Dominating Set
Reconfiguration
Bandwidth
Cardinality
Graph in graph theory
Cographs
Split Graph
Interval Graphs
Graph Classes
Linear-time Algorithm
Decision problem
Bipartite Graph
Planar graph
Deletion
Linear Time
Vertex of a graph

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Haddadan, A., Ito, T., Mouawad, A. E., Nishimura, N., Ono, H., Suzuki, A., & Tebbal, Y. (2016). The complexity of dominating set reconfiguration. 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.

In: Theoretical Computer Science, Vol. 651, 25.10.2016, p. 37-49.

Research output: Contribution to journalArticle

Haddadan, A, Ito, T, Mouawad, AE, Nishimura, N, Ono, H, Suzuki, A & Tebbal, Y 2016, 'The complexity of dominating set reconfiguration', Theoretical Computer Science, vol. 651, pp. 37-49. https://doi.org/10.1016/j.tcs.2016.08.016
Haddadan A, Ito T, Mouawad AE, Nishimura N, Ono H, Suzuki A et al. The complexity of dominating set reconfiguration. Theoretical Computer Science. 2016 Oct 25;651:37-49. https://doi.org/10.1016/j.tcs.2016.08.016
Haddadan, Arash ; Ito, Takehiro ; Mouawad, Amer E. ; Nishimura, Naomi ; Ono, Hirotaka ; Suzuki, Akira ; Tebbal, Youcef. / The complexity of dominating set reconfiguration. In: Theoretical Computer Science. 2016 ; Vol. 651. pp. 37-49.
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