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Homogeneous sets and domination problems

  • Falk Nicolai
  • Thomas Szymczak
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1197)

Abstract

In this paper we consider the relation of homogeneous sets (sometimes called modules) to the domination problems r-dominating clique and connected r-dominating set by investigating homogeneous extensions of graphs.

At first, we show that homogeneous extensions of a hereditary graph class \(\mathcal{G}\)can be recognized nearly as efficiently as the graphs of \(\mathcal{G}\), itself. The algorithm is based on modular decomposition.

In the main part of this work we show, that efficient algorithms solving the r-dominating clique and the connected r-dominating set problem (and thus the Steiner tree problem) on a hereditary graph class \(\mathcal{G}\)lead to efficient algorithms on their homogeneous extensions.

Applying these results to homogeneous extensions of trees we get efficient algorithms solving these problems in linear sequential and polylogarithmic parallel time using a linear number of processors.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Falk Nicolai
    • 1
  • Thomas Szymczak
    • 2
  1. 1.FB Mathematik, FG InformatikGerhard-Mercator-Universität - GH DuisburgDuisburgGermany
  2. 2.FB Informatik, Lehrstuhl für Theoretische InformatikUniversität RostockRostockGermany

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