The min-dist location selection and facility replacement queries

We propose and study a new type of location optimization problem, the min-dist location selection 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. The problem has a wide range of applications in urban development simulation, massively multiplayer online games, and decision support systems. We also investigate a variant of the problem, where we consider replacing (instead of adding) a facility while achieving the same optimization goal. We call this variant the min-dist facility replacement problem. We explore two common approaches to location optimization problems and present methods based on those approaches for solving the min-dist location selection 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 then utilize the key idea behind MND to approach the min-dist facility replacement problem, which results in two algorithms names MSND and RID. We provide a detailed comparative cost analysis and conduct extensive experiments on the various algorithms. The results show that MND and RID outperform their competitors by orders of magnitude.