Optimal Succinct Representations of Planar Maps

Abstract : This paper addresses the problem of representing the connectivity information of geometric objects using as little memory as possible. As opposed to raw compression issues, the focus is here on designing data structures that preserve the possibility of answering incidence queries in constant time. We propose in particular the first optimal representations for 3-connected planar graphs and triangulations, which are the most standard classes of graphs underlying meshes with spherical topology. Optimal means that these representations asymptotically match the respective entropy of the two classes, namely 2 bits per edge for 3-connected planar graphs, and 1.62 bits per triangle or equivalently 3.24 bits per vertex for triangulations.
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Communication dans un congrès
Proc. 22th Annu. Symposium on Computational Geometry, Jun 2006, Sedona, Arizona, United States. ACM, 2006
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Contributeur : Olivier Devillers <>
Soumis le : lundi 25 septembre 2006 - 18:59:37
Dernière modification le : jeudi 10 mai 2018 - 02:06:31
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  • HAL Id : inria-00098669, version 1

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Luca Castelli Aleardi, Olivier Devillers, Gilles Schaeffer. Optimal Succinct Representations of Planar Maps. Proc. 22th Annu. Symposium on Computational Geometry, Jun 2006, Sedona, Arizona, United States. ACM, 2006. 〈inria-00098669〉

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