A Distributed Greedy Heuristic for Computing Voronoi Tessellations with Applications Towards Peer-to-Peer Networks

Abstract

Computing Voronoi tessellations in an arbitrary number of dimensions is a computationally difficult task. This problem becomes exacerbated in distributed environments, such as Peer-to-Peer networks and Wireless networks, where Voronoi tessellations have useful applications. We present our Distributed Greedy Voronoi Heuristic, which approximates Voronoi tessellations in distributed environments. Our heuristic is fast, scalable, works in any geometric space with a distance and midpoint function, and has interesting applications in embedding metrics such as latency in the links of a distributed network.