Quicker Similarity Joins in Metric Spaces

We consider the join operation in metric spaces. Given two sets A and B of objects drawn from some universe U, we want to compute the set A  B = {(a, b) ∈ A × B | d(a, b) ≤ r} efficiently, where d : U×U → R is a metric distance function and r ∈ R is user supplied query radius. In particular we are interested in the case where we have no index available (nor we can afford to build it) for either A or B. In this paper we improve the Quickjoin algorithm (Jacox and Samet, 2008), based on the well-know Quicksort algorithm, by (i) replacing the low level component that handles small subsets with essentially brute-force nested loop with a more efficient method; (ii) showing that, contrary to Quicksort, in Quickjoin unbalanced partitioning can improve the algorithm; and (iii) making the algorithm probabilistic while still obtaining most of the relevant results. We also show how to use Quickjoin to compute k-nearest neighbor joins. The experimental results show that the method works well in practice.