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Solving Connected Dominating Set Faster Than 2n

  • Fedor V. Fomin
  • Fabrizio Grandoni
  • Dieter Kratsch
Part of the Lecture Notes in Computer Science book series (LNCS, 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(2 n ) 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 2 n barrier, by presenting a simple O(1.9407 n ) 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.

Keywords

Exact Algorithm Reduction Rule Free Node Exponential Time Algorithm Algorithm Halt 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Fedor V. Fomin
    • 1
  • Fabrizio Grandoni
    • 2
  • Dieter Kratsch
    • 3
  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.Dipartimento di InformaticaUniversità di Roma “La Sapienza”RomaItaly
  3. 3.LITAUniversité Paul Verlaine – MetzMetz Cedex 01France

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