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All-pairs set similarity is a widely used data mining task, even for largeand high-dimensional datasets. Traditionally, similarity search has focused ondiscovering very similar pairs, for which a variety of efficient algorithms areknown. However, recent work highlights the importance of finding pairs of setswith relatively small intersection sizes. For example, in a recommender system,two users may be alike even though their interests only overlap on a smallpercentage of items. In such systems, some dimensions are often highly skewedbecause they are very popular. Together these two properties render previousapproaches infeasible for large input sizes. To address this problem, wepresent a new distributed algorithm, LSF-Join, for approximate all-pairs setsimilarity. The core of our algorithm is a randomized selection procedure basedon Locality Sensitive Filtering. Our method deviates from prior approximatealgorithms, which are based on Locality Sensitive Hashing. Theoretically, weshow that LSF-Join efficiently finds most close pairs, even for smallsimilarity thresholds and for skewed input sets. We prove guarantees on thecommunication, work, and maximum load of LSF-Join, and we also experimentallydemonstrate its accuracy on multiple graphs.

LSF-Join: Locality Sensitive Filtering for Distributed All-Pairs Set Similarity Under Skew