Dominating set counting in graph classes

Shuji Kijima; Yoshio Okamoto; Takeaki Uno

doi:10.1007/978-3-642-22685-4_2

Dominating set counting in graph classes

Shuji Kijima, Yoshio Okamoto, Takeaki Uno

Mathematical Informatics

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

10 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 language	English
Title of host publication	Computing and Combinatorics - 17th Annual International Conference, COCOON 2011, Proceedings
Pages	13-24
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-642-22685-4_2
Publication status	Published - 2011
Event	17th Annual International Computing and Combinatorics Conference, COCOON 2011 - Dallas, TX, United States Duration: Aug 14 2011 → Aug 16 2011

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	6842 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	17th Annual International Computing and Combinatorics Conference, COCOON 2011
Country/Territory	United States
City	Dallas, TX
Period	8/14/11 → 8/16/11

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-642-22685-4_2

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 proceeding › Conference 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

@inproceedings{6c21ee782d6c4ad68d168665c1313c50,

title = "Dominating set counting in graph classes",

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.",

author = "Shuji Kijima and Yoshio Okamoto and Takeaki Uno",

note = "Funding Information: The first and second authors are supported by Grant-in-Aid for Scientific Research from Ministry of Education, Science and Culture, Japan, and Japan Society for the Promotion of Science.; 17th Annual International Computing and Combinatorics Conference, COCOON 2011 ; Conference date: 14-08-2011 Through 16-08-2011",

year = "2011",

doi = "10.1007/978-3-642-22685-4_2",

language = "English",

isbn = "9783642226847",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

pages = "13--24",

booktitle = "Computing and Combinatorics - 17th Annual International Conference, COCOON 2011, Proceedings",

}

TY - GEN

T1 - Dominating set counting in graph classes

AU - Kijima, Shuji

AU - Okamoto, Yoshio

AU - Uno, Takeaki

N1 - Funding Information: The first and second authors are supported by Grant-in-Aid for Scientific Research from Ministry of Education, Science and Culture, Japan, and Japan Society for the Promotion of Science.

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=80051982070&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80051982070&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-22685-4_2

DO - 10.1007/978-3-642-22685-4_2

M3 - Conference contribution

AN - SCOPUS:80051982070

SN - 9783642226847

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

SP - 13

EP - 24

BT - Computing and Combinatorics - 17th Annual International Conference, COCOON 2011, Proceedings

T2 - 17th Annual International Computing and Combinatorics Conference, COCOON 2011

Y2 - 14 August 2011 through 16 August 2011

ER -

Dominating set counting in graph classes

Abstract

Publication series

Other

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this