Quicker Similarity Joins in Metric Spaces

Abstract

We consider the join operation in metric spaces. Given two sets A and B of objects drawn from some universe $\mathbb U$, we want to compute the set $A \Join B = \{(a,b) \in A \times B\;|\;d(a,b) \leq r\}$ efficiently, where $d : \mathbb U \times \mathbb U \to \mathbb R^+$ 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.