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(Total) Vector domination for graphs with bounded branchwidth

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Title: (Total) Vector domination for graphs with bounded branchwidth
Authors: Ishii, Toshimasa Browse this author →KAKEN DB
Ono, Hirotaka Browse this author →KAKEN DB
Uno, Yushi Browse this author →KAKEN DB
Keywords: Vector dominating set
Total vector dominating set
Multiple dominating set
Bounded branchwidth
Issue Date: 10-Jul-2016
Publisher: Elsevier
Journal Title: Discrete applied mathematics
Volume: 207
Start Page: 80
End Page: 89
Publisher DOI: 10.1016/j.dam.2016.03.002
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 subset of V such that every vertex nu in V \ S (resp., in V) has at least d(nu) 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. (C) 2016 Elsevier B.V. All rights reserved.
Type: article (author version)
Appears in Collections:経済学院・経済学研究院 (Graduate School of Economics and Business / Faculty of Economics and Business) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 石井 利昌

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