(Total) Vector domination for graphs with bounded branchwidth

Toshimasa Ishii, Hirotaka Ono, Yushi Uno

Research output: Contribution to journalArticle

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
Pages (from-to)80-89
Number of pages10
JournalDiscrete Applied Mathematics
Volume207
DOIs
Publication statusPublished - Jul 10 2016

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

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

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

In: Discrete Applied Mathematics, Vol. 207, 10.07.2016, p. 80-89.

Research output: Contribution to journalArticle

Ishii, Toshimasa ; Ono, Hirotaka ; Uno, Yushi. / (Total) Vector domination for graphs with bounded branchwidth. In: Discrete Applied Mathematics. 2016 ; Vol. 207. pp. 80-89.
@article{ddb1458b178a41999b563e1feb7a83bb,
title = "(Total) Vector domination for graphs with bounded branchwidth",
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.",
author = "Toshimasa Ishii and Hirotaka Ono and Yushi Uno",
year = "2016",
month = "7",
day = "10",
doi = "10.1016/j.dam.2016.03.002",
language = "English",
volume = "207",
pages = "80--89",
journal = "Discrete Applied Mathematics",
issn = "0166-218X",
publisher = "Elsevier",

}

TY - JOUR

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

AU - Ishii, Toshimasa

AU - Ono, Hirotaka

AU - Uno, Yushi

PY - 2016/7/10

Y1 - 2016/7/10

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=84979457604&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84979457604&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2016.03.002

DO - 10.1016/j.dam.2016.03.002

M3 - Article

AN - SCOPUS:84979457604

VL - 207

SP - 80

EP - 89

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -