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

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.