# Succinct representation of triangulations with a boundary

2 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We consider the problem of designing succinct geometric data structures while maintaining efficient navigation operations. A data structure is said succinct if the asymptotic amount of space it uses matches the entropy of the class of structures represented. For the case of planar triangulations with a boundary we propose a succinct representation of the combinatorial information that improves to 2.175 bits per triangle the asymptotic amount of space required and that supports the navigation between adjacent triangles in constant time (as well as other standard operations). For triangulations with $m$ faces of a surface with genus g, our representation requires asymptotically an extra amount of 36(g-1)lg m bits (which is negligible as long as g << m/lg m).
Document type :
Conference papers

Cited literature [14 references]

https://hal.inria.fr/inria-00090707
Contributor : Olivier Devillers <>
Submitted on : Friday, September 1, 2006 - 3:06:16 PM
Last modification on : Thursday, March 5, 2020 - 6:28:04 PM
Long-term archiving on: : Tuesday, April 6, 2010 - 12:44:30 AM

### Identifiers

• HAL Id : inria-00090707, version 1

### Citation

Luca Castelli Aleardi, Olivier Devillers, Gilles Schaeffer. Succinct representation of triangulations with a boundary. 9th Workshop on Algorithms and Data Structures, Aug 2005, Waterloo, Canada, pp.134--135. ⟨inria-00090707⟩

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