The complexity of dominating set reconfiguration

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

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

7 Citations (Scopus)

Abstract

Suppose that we are given two dominating sets Ds and Dt 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 Ds and Dt 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, trees, 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
Title of host publicationAlgorithms and Data Structures - 14th International Symposium, WADS 2015, Proceedings
EditorsFrank Dehne, Jorg-Rudiger Sack, Ulrike Stege
PublisherSpringer Verlag
Pages398-409
Number of pages12
ISBN (Print)9783319218397
DOIs
Publication statusPublished - Jan 1 2015
Event14th International Symposium on Algorithms and Data Structures, WADS 2015 - Victoria, Canada
Duration: Aug 5 2015Aug 7 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9214
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other14th International Symposium on Algorithms and Data Structures, WADS 2015
CountryCanada
CityVictoria
Period8/5/158/7/15

Fingerprint

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. (2015). The complexity of dominating set reconfiguration. In F. Dehne, J-R. Sack, & U. Stege (Eds.), Algorithms and Data Structures - 14th International Symposium, WADS 2015, Proceedings (pp. 398-409). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9214). Springer Verlag. https://doi.org/10.1007/978-3-319-21840-3_33

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

Algorithms and Data Structures - 14th International Symposium, WADS 2015, Proceedings. ed. / Frank Dehne; Jorg-Rudiger Sack; Ulrike Stege. Springer Verlag, 2015. p. 398-409 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9214).

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

Haddadan, A, Ito, T, Mouawad, AE, Nishimura, N, Ono, H, Suzuki, A & Tebbal, Y 2015, The complexity of dominating set reconfiguration. in F Dehne, J-R Sack & U Stege (eds), Algorithms and Data Structures - 14th International Symposium, WADS 2015, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9214, Springer Verlag, pp. 398-409, 14th International Symposium on Algorithms and Data Structures, WADS 2015, Victoria, Canada, 8/5/15. https://doi.org/10.1007/978-3-319-21840-3_33
Haddadan A, Ito T, Mouawad AE, Nishimura N, Ono H, Suzuki A et al. The complexity of dominating set reconfiguration. In Dehne F, Sack J-R, Stege U, editors, Algorithms and Data Structures - 14th International Symposium, WADS 2015, Proceedings. Springer Verlag. 2015. p. 398-409. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-21840-3_33
Haddadan, Arash ; Ito, Takehiro ; Mouawad, Amer E. ; Nishimura, Naomi ; Ono, Hirotaka ; Suzuki, Akira ; Tebbal, Youcef. / The complexity of dominating set reconfiguration. Algorithms and Data Structures - 14th International Symposium, WADS 2015, Proceedings. editor / Frank Dehne ; Jorg-Rudiger Sack ; Ulrike Stege. Springer Verlag, 2015. pp. 398-409 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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