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The SPQR-Tree Data Structure in Graph Drawing

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Automata, Languages and Programming (ICALP 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2719))

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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 [13] based on ideas by Bienstock and Monma [[9], [10]]. For planar graphs, SPQR-trees have the nice property to represent the set of all its combinatorial embeddings. Therefore, the data structure has mainly (but not only) been used in the area of planar graph algorithms and graph layout.

The techniques are quite manifold, reaching from special purpose algorithms that merge the solutions of the triconnected components in a clever way to a solution of the original graph, to general branch-and-bound techniques and integer linear programming techniques. Applications reach from Steiner tree problems, to on-line problems in a dynamic setting as well as problems concerned with planarity and graph drawing. This paper gives a survey on the use of SPQR-trees in graph algorithms, with a focus on graph drawing.

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Author information

Authors and Affiliations

  1. Vienna University of Technology, Karlsplatz 13 E186, A-1040, Vienna, Austria

    Petra Mutzel

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  1. Petra Mutzel
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Editors and Affiliations

  1. Dept. of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Jos C. M. Baeten

  2. School of Industrial and Systems Engineering, Georgia Institute of Technology, 765 Ferst Drive, Atlanta, GA, 30332-0205, USA

    Jan Karel Lenstra

  3. Department of Information Technology, Uppsala University, P.O. Box 337, 75105, Uppsala, Sweden

    Joachim Parrow

  4. Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Gerhard J. Woeginger

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Mutzel, P. (2003). The SPQR-Tree Data Structure in Graph Drawing. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds) Automata, Languages and Programming. ICALP 2003. Lecture Notes in Computer Science, vol 2719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45061-0_4

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  • DOI: https://doi.org/10.1007/3-540-45061-0_4

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