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(Total) Vector Domination for Graphs with Bounded Branchwidth

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LATIN 2014: Theoretical Informatics (LATIN 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8392))

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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.

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Author information

Authors and Affiliations

  1. Graduate School of Economics and Business Administration, Hokkaido University, Sapporo, 060-0809, Japan

    Toshimasa Ishii

  2. Department of Economic Engineering, Faculty of Economics, Kyushu University, Fukuoka, 812-8581, Japan

    Hirotaka Ono

  3. Department of Mathematics and Information Sciences, Graduate School of Science, Osaka Prefecture University, Sakai, 599-8531, Japan

    Yushi Uno

Authors
  1. Toshimasa Ishii
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  2. Hirotaka Ono
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  3. Yushi Uno
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Editors and Affiliations

  1. Facultad de Ingeniería, Instituto de Computación, Universidad de la República, Julio Herrera y Reissig 565, 11300, Montevideo, Uruguay

    Alberto Pardo  & Alfredo Viola  & 

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Ishii, T., Ono, H., Uno, Y. (2014). (Total) Vector Domination for Graphs with Bounded Branchwidth. In: Pardo, A., Viola, A. (eds) LATIN 2014: Theoretical Informatics. LATIN 2014. Lecture Notes in Computer Science, vol 8392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54423-1_21

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  • DOI: https://doi.org/10.1007/978-3-642-54423-1_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54422-4

  • Online ISBN: 978-3-642-54423-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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