Partial vs. Complete Domination: t-Dominating Set

  • Authors:

  • Joachim Kneis;Daniel Mölle;Peter Rossmanith

  • Affiliations:

  • Department of Computer Science, RWTH Aachen University, Germany;Department of Computer Science, RWTH Aachen University, Germany;Department of Computer Science, RWTH Aachen University, Germany

  • Venue:
  • SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science
  • Year:
  • 2007

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Abstract

We examine the parameterized complexity of t-Dominating Set, the problem of finding a set of at most knodes that dominate at least tnodes of a graph G= (V,E). The classic NP-complete problem Dominating Set, which can be seen to be t-Dominating Setwith 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 Setand the parameter k, we are able to prove fixed-parameter tractability for t-Dominating Setand 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.