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International Conference on Foundations of Software Technology and Theoretical Computer Science

FSTTCS 2006: FSTTCS 2006: Foundations of Software Technology and Theoretical Computer Science pp 152–163Cite as

Solving Connected Dominating Set Faster Than 2n

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4337))

Abstract

In the connected dominating set problem we are given an n-node undirected graph, and we are asked to find a minimum cardinality connected subset S of nodes such that each node not in S is adjacent to some node in S. This problem is also equivalent to finding a spanning tree with maximum number of leaves.

Despite its relevance in applications, the best known exact algorithm for the problem is the trivial Ω(2n) algorithm which enumerates all the subsets of nodes. This is not the case for the general (unconnected) version of the problem, for which much faster algorithms are available. Such difference is not surprising, since connectivity is a global property, and non-local problems are typically much harder to solve exactly.

In this paper we break the 2n barrier, by presenting a simple O(1.9407n) algorithm for the connected dominating set problem. The algorithm makes use of new domination rules, and its analysis is based on the Measure and Conquer technique.

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Author information

Authors and Affiliations

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

    Fedor V. Fomin

  2. Dipartimento di Informatica, Università di Roma “La Sapienza”, Via Salaria 113, 00198, Roma, Italy

    Fabrizio Grandoni

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

    Dieter Kratsch

Authors
  1. Fedor V. Fomin
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  2. Fabrizio Grandoni
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  3. Dieter Kratsch
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology Delhi, P.O. Box, 110016, New Delhi, India

    S. Arun-Kumar

  2. Indian Institute of Technology, Delhi

    Naveen Garg

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Fomin, F.V., Grandoni, F., Kratsch, D. (2006). Solving Connected Dominating Set Faster Than 2n . In: Arun-Kumar, S., Garg, N. (eds) FSTTCS 2006: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2006. Lecture Notes in Computer Science, vol 4337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11944836_16

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  • DOI: https://doi.org/10.1007/11944836_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-49994-7

  • Online ISBN: 978-3-540-49995-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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