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Summary: Dynamic updates of succinct triangulations #
Luca Castelli Aleardi + Olivier Devillers # Gilles Schae#er §
Abstract
In a recent article, we presented a succinct representa
tion of triangulations that supports e#cient navigation
operations. Here this representation is improved to al
low for e#cient local updates of the triangulations.
Precisely, we show how a succinct representation of
a triangulation with m triangles can be maintained un
der 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).
1 Introduction
Data structures are usually based on explicit pointer
representations. For instance, a binary tree is typically
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