The Min-dist Location Selection Query

We propose and study a new type of location optimization problem: given a set of clients and a set of existing facilities, we select a location from a given set of potential locations for establishing a new facility so that the average distance between a client and her nearest facility is minimized. We call this problem the min-dist location selection problem, which has a wide range of applications in urban development simulation, massively multiplayer online games, and decision support systems. We explore two common approaches to location optimization problems and propose methods based on those approaches for solving this new problem. However, those methods either need to maintain an extra index or fall short in efficiency. To address their drawbacks, we propose a novel method (named MND), which has very close performance to the fastest method but does not need an extra index. We provide a detailed comparative cost analysis on the various algorithms. We also perform extensive experiments to evaluate their empirical performance and validate the efficiency of the MND method.