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(Total) Vector Domination for Graphs with Bounded Branchwidth

  • Toshimasa Ishii
  • Hirotaka Ono
  • Yushi Uno
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8392)

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.

Keywords

Planar Graph Time Algorithm Dynamic Programming Algorithm Minimum Vector Solution Size 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Toshimasa Ishii
    • 1
  • Hirotaka Ono
    • 2
  • Yushi Uno
    • 3
  1. 1.Graduate School of Economics and Business AdministrationHokkaido UniversitySapporoJapan
  2. 2.Department of Economic Engineering, Faculty of EconomicsKyushu UniversityFukuokaJapan
  3. 3.Department of Mathematics and Information Sciences, Graduate School of ScienceOsaka Prefecture UniversitySakaiJapan

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