Fine-grain discrete Voronoi diagram algorithms in L1 and L∞ norms

Authors:
W. A. Maniatty;B. K. Szymanski
Affiliations:
Computer Science Department, Rensselaer Polytechnic Institute Troy, NY 12180, U.S.A.;Computer Science Department, Rensselaer Polytechnic Institute Troy, NY 12180, U.S.A.
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
1997

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Abstract

The well-known Voronoi diagram problem partitions a space containing a finite set of points, P, in such a way that each partition contains a single point in P and the subspace for which it is the nearest point from the set. Adamatzky defined the Discrete Voronoi Diagram (DVD) problem as finding the Voronoi diagram in a discrete lattice. Adamatzky proposed some efficient algorithms for computing DVDs on fine grained synchronous single instruction multiple data (SIMD) mesh architectures when either the L"1 or the L"~ distance metric is used. This paper presents improvements to Adamatzky's algorithms that ensure their correctness without increasing their complexity.