Fast k-clustering queries on embeddings of road networks

In this paper, we study the k-clustering query problem on road networks, an important problem in Geographic Information Systems ("GIS"). Using previously developed Euclidean embeddings and reduction to fast nearest neighbor search, we show and analyze approximation algorithms for these problems. Since these problems are difficult to solve exactly --- and even hard to approximate for most variants --- we compare our constant factor approximation algorithms to exact answers on small synthetic datasets and on a dataset representing Tallahassee, Florida, a small city. We have implemented a web application that demonstrates our method for road networks in the same small city.