### 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 language | English |
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Title of host publication | LATIN 2014 |

Subtitle of host publication | Theoretical Informatics - 11th Latin American Symposium, Proceedings |

Publisher | Springer Verlag |

Pages | 238-249 |

Number of pages | 12 |

ISBN (Print) | 9783642544224 |

DOIs | |

Publication status | Published - Jan 1 2014 |

Event | 11th Latin American Theoretical Informatics Symposium, LATIN 2014 - Montevideo, Uruguay Duration: Mar 31 2014 → Apr 4 2014 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 8392 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 11th Latin American Theoretical Informatics Symposium, LATIN 2014 |
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Country | Uruguay |

City | Montevideo |

Period | 3/31/14 → 4/4/14 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*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.

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

*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

}

TY - GEN

T1 - (Total) vector domination for graphs with bounded branchwidth

AU - Ishii, Toshimasa

AU - Ono, Hirotaka

AU - Uno, Yushi

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84899994628&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84899994628&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-54423-1_21

DO - 10.1007/978-3-642-54423-1_21

M3 - Conference contribution

AN - SCOPUS:84899994628

SN - 9783642544224

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

SP - 238

EP - 249

BT - LATIN 2014

PB - Springer Verlag

ER -