Dynamic updates of succinct triangulations

Abstract : In a recent article, we presented a succinct representation of triangulations that supports efficient navigation operations. Here this representation is improved to allow for efficient local updates of the triangulations. Precisely, we show how a succinct representation of a triangulation with $m$ triangles can be maintained under vertex insertions in $O(1)$ amortized time and under vertex deletions/edge flips in $O(lg^2 m)$ amortized time. Our structure achieves the information theory bound for the storage for the class of triangulations with a boundary, requiring asymptotically $2.17m+o(m)$ bits, and supports adjacency queries between triangles in $O(1)$ time (an extra amount of $O(g lgm)$ bits are needed for representing triangulations of genus $g$ surfaces).
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https://hal.inria.fr/inria-00070308
Contributor : Rapport de Recherche Inria <>
Submitted on : Friday, May 19, 2006 - 8:00:06 PM
Last modification on : Wednesday, March 27, 2019 - 4:41:27 PM
Long-term archiving on : Sunday, April 4, 2010 - 8:54:00 PM

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  • HAL Id : inria-00070308, version 1

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Luca Castelli Aleardi, Olivier Devillers, Gilles Schaeffer. Dynamic updates of succinct triangulations. [Research Report] RR-5709, INRIA. 2006, pp.23. ⟨inria-00070308⟩

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