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An Exact Algorithm for the Minimum Dominating Clique Problem

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Book cover Parameterized and Exact Computation (IWPEC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4169))

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Abstract

A subset of vertices D ⊆ V of a graph G = (V,E) is a dominating clique if D is a dominating set and a clique of G. The existence problem ‘Given a graph G, is there a dominating clique in G?’ is NP-complete, and thus both the Minimum and the Maximum Dominating Clique problem are NP-hard. We present an O(1.3390n) time algorithm that for an input graph on n vertices either computes a minimum dominating clique or reports that the graph has no dominating clique. The algorithm uses the Branch & Reduce paradigm and its time analysis is based on the Measure & Conquer approach. We also establish a lower bound of Ω(1.2599n) for the worst case running time of our algorithm.

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Author information

Authors and Affiliations

  1. LITA, Université Paul Verlaine – Metz, 57045 Cedex 01, Metz, France

    Dieter Kratsch & Mathieu Liedloff

Authors
  1. Dieter Kratsch
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  2. Mathieu Liedloff
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Editor information

Editors and Affiliations

  1. Department of Information and Computing Sciences, Utrecht University, The Netherlands

    Hans L. Bodlaender

  2. University of Tennessee, 37996-3450, Knoxville, Tennessee, U.S.A.

    Michael A. Langston

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© 2006 Springer-Verlag Berlin Heidelberg

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Kratsch, D., Liedloff, M. (2006). An Exact Algorithm for the Minimum Dominating Clique Problem. In: Bodlaender, H.L., Langston, M.A. (eds) Parameterized and Exact Computation. IWPEC 2006. Lecture Notes in Computer Science, vol 4169. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11847250_12

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  • DOI: https://doi.org/10.1007/11847250_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-39098-5

  • Online ISBN: 978-3-540-39101-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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