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International Symposium on Parameterized and Exact Computation

IPEC 2011: Parameterized and Exact Computation pp 41–54Cite as

A Faster Algorithm for Dominating Set Analyzed by the Potential Method

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7112))

Abstract

Measure and Conquer is a recently developed technique to analyze worst-case complexity of backtracking algorithms. The traditional measure and conquer analysis concentrates on one branching at once by using only small number of variables. In this paper, we extend the measure and conquer analysis and introduce a new analyzing technique named “potential method” to deal with consecutive branchings together. In potential method, the optimization problem becomes sparse; therefore, we can use large number of variables. We applied this technique to the minimum dominating set problem and obtained the current fastest algorithm that runs in O(1.4864n) time and polynomial space. We also combined this algorithm with a precalculation by dynamic programming and obtained O(1.4689n) time and space algorithm. These results show the power of the potential method and possibilities of future applications to other problems.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, Japan

    Yoichi Iwata

Authors
  1. Yoichi Iwata
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Editor information

Editors and Affiliations

  1. MTA SZTAKI, Lágymányosi u. 11, 1111, Budapest, Hungary

    Dániel Marx

  2. Lehrgebiet Theoretische Informatik, RWTH Aachen, Ahornstraße 55, 52056, Aachen, Germany

    Peter Rossmanith

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Iwata, Y. (2012). A Faster Algorithm for Dominating Set Analyzed by the Potential Method. In: Marx, D., Rossmanith, P. (eds) Parameterized and Exact Computation. IPEC 2011. Lecture Notes in Computer Science, vol 7112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28050-4_4

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  • DOI: https://doi.org/10.1007/978-3-642-28050-4_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28049-8

  • Online ISBN: 978-3-642-28050-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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