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Solving Connected Dominating Set Faster than 2n

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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 that 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 a 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, 5020, Bergen, Norway

    Fedor V. Fomin

  2. Dipartimento di Informatica, Università di Roma “La Sapienza”, via Salaria 113, 00198, Rome, 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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Corresponding author

Correspondence to Dieter Kratsch.

Additional information

An extended abstract of this paper appeared in the proceedings of FSTTCS’06.

Fedor V. Fomin was additionally supported by the Research Council of Norway.

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Fomin, F.V., Grandoni, F. & Kratsch, D. Solving Connected Dominating Set Faster than 2n . Algorithmica 52, 153–166 (2008). https://doi.org/10.1007/s00453-007-9145-z

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