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Inclusion/Exclusion Branching for Partial Dominating Set and Set Splitting

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Parameterized and Exact Computation (IPEC 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6478))

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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.

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Author information

Authors and Affiliations

  1. Department of Informatics, University of Bergen, N-5020, Bergen, Norway

    Jesper Nederlof

  2. Department of Information and Computing Sciences, Utrecht University, P.O. Box 80.089, 3508 TB, Utrecht, The Netherlands

    Johan M. M. van Rooij

Authors
  1. Jesper Nederlof
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  2. Johan M. M. van Rooij
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Editor information

Editors and Affiliations

  1. The Institute of Mathematical Sciences, Chennai, India

    Venkatesh Raman

  2. The Institute of Mathematical Sciences, 600113, Chennai, India

    Saket Saurabh

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Nederlof, J., van Rooij, J.M.M. (2010). Inclusion/Exclusion Branching for Partial Dominating Set and Set Splitting. In: Raman, V., Saurabh, S. (eds) Parameterized and Exact Computation. IPEC 2010. Lecture Notes in Computer Science, vol 6478. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17493-3_20

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  • DOI: https://doi.org/10.1007/978-3-642-17493-3_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17492-6

  • Online ISBN: 978-3-642-17493-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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