Asynchronous Computing of a Discrete Voronoi Diagram on a Cellular Automaton Using 1-Norm: Application to Roadmap Extraction

Abstract

This article addresses the problem of computing a Voronoi diagram in a distributed fashion without any synchronization heuristic. To our knowledge, no previous work asynchronously solves this problem. We investigate a simple case of a synchronism and tackle this challenge in a decentralized fashion on a grid of communicating cells with a von Neumann neighborhood. We describe algorithms for extracting single site, area and pseudo line Voronoi diagrams. These algorithms are implemented and executed on maps in which we consider different kinds of sites defined as simple polygonal shapes to extract roadmaps.