Dominating set counting in graph classes

Shuji Kijima, Yoshio Okamoto, Takeaki Uno

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

7 Citations (Scopus)

Abstract

We make an attempt to understand the dominating set counting problem in graph classes from the viewpoint of polynomial-time computability. We give polynomial-time algorithms to count the number of dominating sets (and minimum dominating sets) in interval graphs and trapezoid graphs. They are based on dynamic programming. With the help of dynamic update on a binary tree, we further reduce the time complexity. On the other hand, we prove that counting the number of dominating sets (and minimum dominating sets) in split graphs and chordal bipartite graphs is #P-complete. These results are in vivid contrast with the recent results on counting the independent sets and the matchings in chordal graphs and chordal bipartite graphs.

Original languageEnglish
Title of host publicationComputing and Combinatorics - 17th Annual International Conference, COCOON 2011, Proceedings
Pages13-24
Number of pages12
DOIs
Publication statusPublished - Aug 29 2011
Event17th Annual International Computing and Combinatorics Conference, COCOON 2011 - Dallas, TX, United States
Duration: Aug 14 2011Aug 16 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6842 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other17th Annual International Computing and Combinatorics Conference, COCOON 2011
CountryUnited States
CityDallas, TX
Period8/14/118/16/11

Fingerprint

Graph Classes
Dominating Set
Counting
Polynomials
Binary trees
Chordal Bipartite Graphs
Dynamic programming
Trapezoid Graph
Split Graph
Counting Problems
Interval Graphs
Chordal Graphs
Computability
Binary Tree
Independent Set
Polynomial-time Algorithm
Time Complexity
Dynamic Programming
Polynomial time
Count

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Kijima, S., Okamoto, Y., & Uno, T. (2011). Dominating set counting in graph classes. In Computing and Combinatorics - 17th Annual International Conference, COCOON 2011, Proceedings (pp. 13-24). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6842 LNCS). https://doi.org/10.1007/978-3-642-22685-4_2

Dominating set counting in graph classes. / Kijima, Shuji; Okamoto, Yoshio; Uno, Takeaki.

Computing and Combinatorics - 17th Annual International Conference, COCOON 2011, Proceedings. 2011. p. 13-24 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6842 LNCS).

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

Kijima, S, Okamoto, Y & Uno, T 2011, Dominating set counting in graph classes. in Computing and Combinatorics - 17th Annual International Conference, COCOON 2011, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6842 LNCS, pp. 13-24, 17th Annual International Computing and Combinatorics Conference, COCOON 2011, Dallas, TX, United States, 8/14/11. https://doi.org/10.1007/978-3-642-22685-4_2
Kijima S, Okamoto Y, Uno T. Dominating set counting in graph classes. In Computing and Combinatorics - 17th Annual International Conference, COCOON 2011, Proceedings. 2011. p. 13-24. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-22685-4_2
Kijima, Shuji ; Okamoto, Yoshio ; Uno, Takeaki. / Dominating set counting in graph classes. Computing and Combinatorics - 17th Annual International Conference, COCOON 2011, Proceedings. 2011. pp. 13-24 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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