An Algorithm to solve a Facility Location Problem using a Discrete Approximation to the Voronoi Diagram

Identifying optimal locations for new facilities is a common, yet paramount, task in fields as diverse as communications (e.g., cell phone towers) to business (e.g., store locations). Problematically, identifying optimal locations is computationally expensive. In this paper, we propose a novel algorithm to solve the facility localization problem based on a parallelizable discrete approximation of a Voronoi diagram, rather than previously considered exact Voronoi diagram calculations. The growth in execution time across increasing numbers of facilities and increasing geographic planes are empirically analyzed. Finally, the execution time of sequential and parallel implementations is compared across a variety of two-dimensional problem sizes illustrating substantial speedup.