A Linear Time Implementation of SPQR-Trees

  • Carsten Gutwenger
  • Petra Mutzel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1984)

Abstract

The data structure SPQR-tree represents the decomposition of a biconnected graph with respect to its triconnected components. SPQR-trees have been introduced by Di Battista and Tamassia [8] and, since then, became quite important in the field of graph algorithms. Theoretical papers using SPQR-trees claim that they can be implemented in linear time using a modification of the algorithm by Hopcroft and Tarjan [15] for decomposing a graph into its triconnected components. So far no correct linear time implementation of either triconnectivity decomposition or SPQR-trees is known to us. Here, we show the incorrectness of the Hopcroft and Tarjan algorithm [15], and correct the faulty parts. We describe the relationship between SPQR-trees and triconnected components and apply the resulting algorithm to the computation of SPQR-trees. Our implementation is publically available in AGD [1].

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Carsten Gutwenger
    • 1
  • Petra Mutzel
    • 2
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany
  2. 2.Technische Universität WienAustria

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