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International Colloquium on Automata, Languages, and Programming

ICALP 2003: Automata, Languages and Programming pp 1080–1094Cite as

Optimal Coding and Sampling of Triangulations

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

Abstract

We present a bijection between the set of plane triangulations (aka. maximal planar graphs) and a simply defined subset of plane trees with two leaves per inner node. The construction takes advantage of the minimal realizer (or Schnyder tree decomposition) of a plane triangulation.

This yields a simple interpretation of the formula for the number of plane triangulations with n vertices. Moreover the construction is simple enough to induce a linear random sampling algorithm, and an explicit information theory optimal encoding.

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Author information

Authors and Affiliations

  1. École polytechnique, LIX — CNRS, 91128, Palaiseau Cedex, France

    Dominique Poulalhon & Gilles Schaeffer

Authors
  1. Dominique Poulalhon
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  2. Gilles Schaeffer
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Editor information

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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© 2003 Springer-Verlag Berlin Heidelberg

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Poulalhon, D., Schaeffer, G. (2003). Optimal Coding and Sampling of Triangulations. 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_83

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  • DOI: https://doi.org/10.1007/3-540-45061-0_83

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40493-4

  • Online ISBN: 978-3-540-45061-0

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