Uncertain Voronoi diagram

Authors:
Mohammadreza Jooyandeh;Ali Mohades;Maryam Mirzakhah
Affiliations:
Faculty of Mathematics and Computer Science, Amirkabir University of Technology, PO Box 15875-4413, Tehran, Iran;Faculty of Mathematics and Computer Science, Amirkabir University of Technology, PO Box 15875-4413, Tehran, Iran;Faculty of Mathematics and Computer Science, Amirkabir University of Technology, PO Box 15875-4413, Tehran, Iran
Venue:
Information Processing Letters
Year:
2009

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Abstract

In this paper, we introduce the fuzzy Voronoi diagram as an extension of the Voronoi diagram. We assume Voronoi sites to be fuzzy points and then define the Voronoi diagram for this kind of sites, then we provide an algorithm for computing this diagram based on Fortune's algorithm which costs O(nlogn) time. Also we introduce the fuzzy Voronoi diagram for a set of fuzzy circles, rather than fuzzy points, of the same radius. We prove that the boundary of this diagram is formed by the intersection of some hyperbolae, and finally we provide an O(n^3logn)-time algorithm to compute the boundary.