Dynamic smooth compressed quadtrees (Fullversion)
Ivor Hoog v.d., Elena Khramtcova, Maarten L\"offler

TL;DR
This paper presents a new type of dynamic, smooth compressed quadtrees that support constant-time updates in fixed dimensions, improving efficiency for geometric data structures and algorithms.
Contribution
The authors introduce dynamic smooth compressed quadtrees with worst-case constant time updates, addressing both space-division and point set storage scenarios.
Findings
Updates take 2^{O(d log d)} time in general
Point location can be optimized with a pointer to the cell
Supports dynamic insertions, deletions, splits, and merges
Abstract
We introduce dynamic smooth (a.k.a. balanced) compressed quadtrees with worst-case constant time updates in constant dimensions. We distinguish two versions of the problem. First, we show that quadtrees as a space-division data structure can be made smooth and dynamic subject to split and merge operations on the quadtree cells. Second, we show that quadtrees used to store a set of points in can be made smooth and dynamic subject to insertions and deletions of points. The second version uses the first but must additionally deal with compression and alignment of quadtree components. In both cases our updates take time, except for the point location part in the second version which has a lower bound of ---but if a pointer (finger) to the correct quadtree cell is given, the rest of the updates take worst-case constant time. Our…
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Taxonomy
TopicsComputer Graphics and Visualization Techniques · Computational Geometry and Mesh Generation · Digital Image Processing Techniques
