In this assignment you are required to implement a system for handling data similar to that used in game programming. In such an environment the primary entities are polygons and the problem we are interested is how to manage a large collection of them. In this assignment, we will restrict input to a collection of small rectangles. In the following we trace the development of a variant of the q...

With a focus on mobile and web mapping, we propose several algorithms for on-the-fly generalization of point data, such as points of interest (POIs) or large point collections. In order to achieve real-time performance we use a quadtree data structure. With their hierarchical subdivision structure and progressive levels of detail, indices of the quadtree family lend themselves as auxiliary data...

Inherent to photograph-like images are two types of structures: large smooth regions and geometrically smooth edge contours separating those regions. Over the past years, efficient representations and algorithms have been developed that take advantage of each of these types of structure independently: quadtree models for 2D wavelets are well-suited for uniformly smooth images (C everywhere), wh...

Relational index structures, as for instance the Relational Interval Tree, the Relational R-Tree, or the Linear Quadtree, support efficient processing of queries on top of existing object-relational database systems. Furthermore, there exist effective and efficient models to estimate the selectivity and the I/O cost in order to guide the cost-based optimizer whether and how to include these ind...

4 We show that Delaunay triangulations and compressed quadtrees are equivalent structures. More precisely, 5 we give two algorithms: the first computes a compressed quadtree for a planar point set, given the Delaunay 6 triangulation; the second finds the Delaunay triangulation, given a compressed quadtree. Both algorithms 7 run in deterministic linear time on a pointer machine. Our work builds ...

This paper studies the parallel construction and manipulation of pointer based quadtrees on the hypercube multiprocessor. While parallel algorithms for the manipulation of a variant of linear quadtrees have been previously studied in the literature, no parallel pointer based quadtree construction algorithms have been presented. In this paper, we solve the problem of efficiently constructing poi...