Succinct representations of planar maps - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Theoretical Computer Science Année : 2008

Succinct representations of planar maps

Résumé

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.
Fichier principal
Vignette du fichier
hal.pdf (578.64 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

inria-00337821 , version 1 (08-11-2008)

Identifiants

Citer

Luca Castelli Aleardi, Olivier Devillers, Gilles Schaeffer. Succinct representations of planar maps. Theoretical Computer Science, 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⟩
209 Consultations
219 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More