Finding the k-closest pairs in metric spaces

Abstract

We investigated the problem of reducing the cost of searching for the k closest pairs in metric spaces. In general, a k-closest pair search method initializes the upper bound distance between the k closest pairs as infinity and repeatedly updates the upper bound distance whenever it finds pairs of objects whose distances are shorter than that distance. Furthermore, it prunes dissimilar pairs whose distances are estimated as longer than the upper bound distance based on the distances from the pivot to objects and the triangle inequality. The cost of a k-closest pair query is smaller for a shorter upper bound distance and a sparser distribution of distances between the pivot and objects. We propose a new divide-and-conquer-based k-closest pair search method in metric spaces, called Adaptive Multi-Partitioning (AMP). AMP repeatedly divides and conquers objects from the sparser distance-distribution space and speeds up the convergence of the upper bound distance before partitioning the denser space. As a result, AMP can prune many dissimilar pairs compared with ordinary divide-and-conquer-based method. We compare our method with other partitioning method and show that AMP reduces distances computations.