Iteratively Locating Voronoi Vertices for Dispersion Estimation

We present a new sampling-based algorithm for iteratively locating Voronoi vertices of a point set in the unit cube I^d= [0, 1]^d. The algorithm takes an input sample and executes a series of transformations, each of which projects the sample to a new face of the Voronoi cell in which it is located. After d such transformations, the sample has been transformed into a Voronoi vertex. Locating Voronoi vertices has many potential applications for motion planning, such as estimating dispersion for coverage and verification applications, and providing information useful for Voronoi-biased or multiple-tree planning. We prove theoretical results regarding our algorithm, and give experimental results comparing it to naive sampling for the problem of dispersion estimation.