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 here is 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. These representations support adjacency queries between vertices and faces in constant time.
Type de document :
Article dans une revue
Theoretical Computer Science, Elsevier, 2008, Excursions in Algorithmics: A Collection of Papers in Honor of Franco P. Preparata, 408 (2-3), pp.174-187. 〈10.1016/j.tcs.2008.08.016〉
Liste complète des métadonnées

Littérature citée [23 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/inria-00337821
Contributeur : Olivier Devillers <>
Soumis le : samedi 8 novembre 2008 - 19:39:40
Dernière modification le : jeudi 17 mai 2018 - 12:52:03
Document(s) archivé(s) le : mardi 9 octobre 2012 - 15:10:51

Fichier

hal.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Luca Castelli Aleardi, Olivier Devillers, Gilles Schaeffer. Succinct representations of planar maps. Theoretical Computer Science, Elsevier, 2008, Excursions in Algorithmics: A Collection of Papers in Honor of Franco P. Preparata, 408 (2-3), pp.174-187. 〈10.1016/j.tcs.2008.08.016〉. 〈inria-00337821〉

Partager

Métriques

Consultations de la notice

418

Téléchargements de fichiers

195