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Hardness, Approximability, and Exact Algorithms for Vector Domination and Total Vector Domination in Graphs

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Fundamentals of Computation Theory (FCT 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6914))

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Abstract

We consider two graph optimization problems called vector domination and total vector domination. In vector domination one seeks a small subset S of vertices of a graph such that any vertex outside S has a prescribed number of neighbors in S. In total vector domination, the requirement is extended to all vertices of the graph. We prove that these problems cannot be approximated to within a factor of clogn, for suitable constants c, unless every problem in NP is solvable in slightly super-polynomial time. We also show that two natural greedy strategies have approximation factors O(logΔ(G)), where Δ(G) is the maximum degree of the graph G. We also provide exact polynomial time algorithms for several classes of graphs. Our results extend, improve, and unify several results previously known in the literature.

Supported in part by “Agencija za raziskovalno dejavnost Republike Slovenije”, research program P1-0285.

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica, University of Salerno, 84084, Fisciano, SA, Italy

    Ferdinando Cicalese & Ugo Vaccaro

  2. UP FAMNIT and UP PINT, University of Primorska, 6000, Koper, Slovenia

    Martin Milanič

Authors
  1. Ferdinando Cicalese
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  2. Martin Milanič
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  3. Ugo Vaccaro
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Editor information

Editors and Affiliations

  1. Department of Informatics, University of Oslo, Postboks 1080 Blindern, 0316, Oslo, Norway

    Olaf Owe  & Martin Steffen  & 

  2. Department of Informatics, University of Bergen, Postboks 7800, 5020, Bergen, Norway

    Jan Arne Telle

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Cicalese, F., Milanič, M., Vaccaro, U. (2011). Hardness, Approximability, and Exact Algorithms for Vector Domination and Total Vector Domination in Graphs. In: Owe, O., Steffen, M., Telle, J.A. (eds) Fundamentals of Computation Theory. FCT 2011. Lecture Notes in Computer Science, vol 6914. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22953-4_25

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  • DOI: https://doi.org/10.1007/978-3-642-22953-4_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22952-7

  • Online ISBN: 978-3-642-22953-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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