Plane-Sweep Algorithms for the K Group Nearest-Neighbor Query

One of the most representative and studied queries in Spatial Databases is the (K) Nearest-Neighbor (NNQ), that discovers the (K) nearest neighbor(s) to a query point. An extension that is important for practical applications is the (K) Group Nearest Neighbor Query (GNNQ), that discovers the (K) nearest neighbor(s) to a group of query points (considering the sum of distances to all the members of the query group). This query has been studied during the recent years, considering data sets indexed by efficient spatial data structures. We study (K) GNNQs, considering non-indexed data sets, since this case is frequent in practical applications. And we present two (RAM-based) Plane-Sweep algorithms, that apply optimizations emerging from the geometric properties of the problem. By extensive experimentation, using real and synthetic data sets, we highlight the most efficient algorithm.