Computing a threaded quadtree from the Delaunay triangulation in linear time

Authors:
Drago Krznaric;Christos Levcopoulos
Affiliations:
Department of Computer Science, Lund University, Box 118, S-221 00 Lund, Sweden;Department of Computer Science, Lund University, Box 118, S-221 00 Lund, Sweden
Venue:
Nordic Journal of Computing
Year:
1998

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Abstract

The quadtree in this paper is a variant in which two nodes are threaded (linked) if they represent equal-sized squares that are sufficiently close to each other. Given the Delaunay triangulation, it is shown that the threaded quadtree can be computed in linear time and space. It is also described how the threaded quadtree can be used to answer certain types of non-trivial range queries in constant time per query, which has applications, for example, in computing the greedy triangulation, the complete linkage clustering, and a constant-factor approximation of minimum weight triangulation. These queries ask for links to and information concerning the contents of growing ranges, including values of functions based on these contents.