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Partial vs. Complete Domination: t-Dominating Set

  • Joachim Kneis
  • Daniel Mölle
  • Peter Rossmanith
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4362)

Abstract

We examine the parameterized complexity of t -Dominating Set, the problem of finding a set of at most k nodes that dominate at least t nodes of a graph G = (V,E). The classic NP-complete problem Dominating Set, which can be seen to be t -Dominating Set with the restriction that t = n, has long been known to be W[2]-complete when parameterized in k. Whereas this implies W[2]-hardness for t -Dominating Set and the parameter k, we are able to prove fixed-parameter tractability for t -Dominating Set and the parameter t. More precisely, we obtain a quintic problem kernel and a randomized \(O((4+\varepsilon)^t\textit{poly}(n))\) algorithm. The algorithm is based on the divide-and-color method introduced to the community earlier this year, rather intuitive and can be derandomized using a standard framework.

Keywords

Success Probability Parameterized Complexity Vertex Cover Recursive Call Polynomial Factor 
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 Berlin Heidelberg 2007

Authors and Affiliations

  • Joachim Kneis
    • 1
  • Daniel Mölle
    • 1
  • Peter Rossmanith
    • 1
  1. 1.Department of Computer Science, RWTH Aachen UniversityGermany

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