Title :
A replacement for Voronoi diagrams of near linear size
Author :
Har-Peled, Sariel
Author_Institution :
Dept. of Comput. Sci., Illinois Univ., Urbana, IL, USA
Abstract :
For a set P of n points in Rd, we define a new type of space decomposition. The new diagram provides an ε-approximation to the distance function associated with the Voronoi diagram of P, while being of near linear size, for d≥2. This contrasts with the standard Voronoi diagram that has Ω (n[d2]/) complexity in the worst case.
Keywords :
computational complexity; computational geometry; set theory; ε-approximation; Voronoi diagram replacement; complexity; distance function; geometric computing; near linear size Voronoi diagrams; space decomposition; standard Voronoi diagram; Artificial intelligence; Chromium; Clustering algorithms; Computer science; Graphics; Mesh generation; Nearest neighbor searches; Neural networks; Polynomials; Surface reconstruction;
Conference_Titel :
Foundations of Computer Science, 2001. Proceedings. 42nd IEEE Symposium on
Print_ISBN :
0-7695-1116-3
DOI :
10.1109/SFCS.2001.959884
