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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Contributor : Olivier Devillers <>
Submitted on : Monday, September 25, 2006 - 6:59:37 PM
Last modification on : Wednesday, July 31, 2019 - 3:23:38 PM
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Luca Castelli Aleardi, Olivier Devillers, Gilles Schaeffer. Optimal Succinct Representations of Planar Maps. Proceedings of the 22nd Annual Symposium on Computational Geometry, Jun 2006, Sedona, Arizona, United States. ⟨10.1145/1137856.1137902⟩. ⟨inria-00098669⟩

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