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Inclusion/Exclusion Branching for Partial Dominating Set and Set Splitting

  • Jesper Nederlof
  • Johan M. M. van Rooij
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6478)

Abstract

Inclusion/exclusion branching is a way to branch on requirements imposed on problems, in contrast to the classical branching on parts of the solution. The technique turned out to be useful for finding and counting (minimum) dominating sets (van Rooij et al., ESA 2009). In this paper, we extend the technique to the setting where one is given a set of properties and seeks (or wants to count) solutions that have at least a given number of these properties. Using this extension, we obtain new algorithms for Partial Dominating Set and the parameterised problem k -Set Splitting. In particular, we apply the new idea to the fastest polynomial space algorithm for counting dominating sets, and directly obtain a polynomial space algorithm for Partial Dominating Set with the same running time (up to a linear factor). Combining the new idea with some previous work, we also give a polynomial space algorithm for k -Set Splitting that improves the fastest known result significantly.

Keywords

Steiner Tree Polynomial Space Incidence Graph Space Algorithm 36th International Colloquium 
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 2010

Authors and Affiliations

  • Jesper Nederlof
    • 1
  • Johan M. M. van Rooij
    • 2
  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.Department of Information and Computing SciencesUtrecht UniversityUtrechtThe Netherlands

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