(Total) vector domination for graphs with bounded branchwidth

Toshimasa Ishii, Hirotaka Ono, Yushi Uno

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

2 Citations (Scopus)

Abstract

Given a graph G= (V,E) of order n and an n-dimensional non-negative vector d= (d(1),d(2), d(n)), called demand vector, the vector domination (resp., total vector domination) is the problem of finding a minimum S⊆ V such that every vertex v in V?S (resp., in V) has at least d(v) neighbors in S. The (total) vector domination is a generalization of many dominating set type problems, e.g., the dominating set problem, the k-tuple dominating set problem (this k is different from the solution size), and so on, and its approximability and inapproximability have been studied under this general framework. In this paper, we show that a (total) vector domination of graphs with bounded branchwidth can be solved in polynomial time. This implies that the problem is polynomially solvable also for graphs with bounded treewidth. Consequently, the (total) vector domination problem for a planar graph is subexponential fixed-parameter tractable with respect to k, where k is the size of solution.

Original languageEnglish
Title of host publicationLATIN 2014
Subtitle of host publicationTheoretical Informatics - 11th Latin American Symposium, Proceedings
PublisherSpringer Verlag
Pages238-249
Number of pages12
ISBN (Print)9783642544224
DOIs
Publication statusPublished - Jan 1 2014
Event11th Latin American Theoretical Informatics Symposium, LATIN 2014 - Montevideo, Uruguay
Duration: Mar 31 2014Apr 4 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8392 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other11th Latin American Theoretical Informatics Symposium, LATIN 2014
CountryUruguay
CityMontevideo
Period3/31/144/4/14

Fingerprint

Branch-width
Domination
Graph in graph theory
Dominating Set
Inapproximability
Bounded Treewidth
Approximability
Planar graph
n-dimensional
Polynomial time
Non-negative
Polynomials
Imply
Vertex of a graph

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Ishii, T., Ono, H., & Uno, Y. (2014). (Total) vector domination for graphs with bounded branchwidth. In LATIN 2014: Theoretical Informatics - 11th Latin American Symposium, Proceedings (pp. 238-249). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8392 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-642-54423-1_21

(Total) vector domination for graphs with bounded branchwidth. / Ishii, Toshimasa; Ono, Hirotaka; Uno, Yushi.

LATIN 2014: Theoretical Informatics - 11th Latin American Symposium, Proceedings. Springer Verlag, 2014. p. 238-249 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8392 LNCS).

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

Ishii, T, Ono, H & Uno, Y 2014, (Total) vector domination for graphs with bounded branchwidth. in LATIN 2014: Theoretical Informatics - 11th Latin American Symposium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8392 LNCS, Springer Verlag, pp. 238-249, 11th Latin American Theoretical Informatics Symposium, LATIN 2014, Montevideo, Uruguay, 3/31/14. https://doi.org/10.1007/978-3-642-54423-1_21
Ishii T, Ono H, Uno Y. (Total) vector domination for graphs with bounded branchwidth. In LATIN 2014: Theoretical Informatics - 11th Latin American Symposium, Proceedings. Springer Verlag. 2014. p. 238-249. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-54423-1_21
Ishii, Toshimasa ; Ono, Hirotaka ; Uno, Yushi. / (Total) vector domination for graphs with bounded branchwidth. LATIN 2014: Theoretical Informatics - 11th Latin American Symposium, Proceedings. Springer Verlag, 2014. pp. 238-249 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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