A Distributed Algorithm for Computing Voronoi Diagram in the Unit Disk Graph Model

We study the problem of computing Voronoi diagrams distributedly for a set of nodes of a network modeled as a Unit Disk Graph (UDG). We present an algorithm to solve this problem efficiently, which has direct applications in wireless networks. Comparing with some existing algorithms, our algorithm correctly computes the complete Voronoi diagram and uses a significantly smaller number of transmissions. Furthermore, useful geometric structures such as the Delaunay triangulation and the convex hull can be obtained through our algorithm.