Optimal succinct representation 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-c planar graphs, and 1.62 bits per triangle or equivalently 3.24 bits per vertex for triangulations.
Document type :
Reports
Complete list of metadatas

Cited literature [1 references]  Display  Hide  Download

https://hal.inria.fr/inria-00070221
Contributor : Rapport de Recherche Inria <>
Submitted on : Friday, May 19, 2006 - 7:31:38 PM
Last modification on : Wednesday, March 27, 2019 - 4:41:27 PM
Long-term archiving on : Sunday, April 4, 2010 - 8:38:42 PM

Identifiers

  • HAL Id : inria-00070221, version 1

Collections

Citation

Luca Castelli Aleardi, Olivier Devillers, Gilles Schaeffer. Optimal succinct representation of planar maps. [Research Report] RR-5803, INRIA. 2006, pp.26. ⟨inria-00070221⟩

Share

Metrics

Record views

528

Files downloads

202