TY - JOUR

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

AU - Ishii, Toshimasa

AU - Ono, Hirotaka

AU - Uno, Yushi

N1 - Funding Information:
This work is partially supported by KAKENHI Nos. 23500022 , 24700001 , 24106004 , 25104521 , 25106508 and 26280001 , the Kayamori Foundation of Informational Science Advancement and The Asahi Glass Foundation .
Publisher Copyright:
© 2016 Elsevier B.V. All rights reserved.

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.

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U2 - 10.1016/j.dam.2016.03.002

DO - 10.1016/j.dam.2016.03.002

M3 - Article

AN - SCOPUS:84979457604

SN - 0166-218X

VL - 207

SP - 80

EP - 89

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -