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 $O(g\lg m)$ bits are needed for representing triangulations of genus $g$ surfaces).
https://hal.inria.fr/inria-00001187
Contributor : Olivier Devillers <>
Submitted on : Wednesday, April 12, 2006 - 2:55:22 PM Last modification on : Tuesday, December 29, 2020 - 7:04:02 AM Long-term archiving on: : Saturday, April 3, 2010 - 10:10:15 PM