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The Exact Set Similarity Join problem aims to find all similar sets betweentwo collections of sets, with respect to a threshold and a similarity functionsuch as overlap, Jaccard, dice or cosine. The naive approach verifies all pairsof sets and it is often considered impractical due the high number ofcombinations. So, Exact Set Similarity Join algorithms are usually based on theFilter-Verification Framework, that applies a series of filters to reduce thenumber of verified pairs. This paper presents a new filtering technique calledBitmap Filter, which is able to accelerate state-of-the-art algorithms for theexact Set Similarity Join problem. The Bitmap Filter uses hash functions tocreate bitmaps of fixed b bits, representing characteristics of the sets. Then,it applies bitwise operations (such as xor and population count) on the bitmapsin order to infer a similarity upper bound for each pair of sets. If the upperbound is below a given similarity threshold, the pair of sets is pruned. TheBitmap Filter benefits from the fact that bitwise operations are efficientlyimplemented by many modern general-purpose processors and it was easily appliedto four state-of-the-art algorithms implemented in CPU: AllPairs, PPJoin,AdaptJoin and GroupJoin. Furthermore, we propose a Graphic Processor Unit (GPU)algorithm based on the naive approach but using the Bitmap Filter to speedupthe computation. The experiments considered 9 collections containing from 100thousands up to 10 million sets and the joins were made using Jaccardthresholds from 0.50 to 0.95. The Bitmap Filter was able to improve 90% of theexperiments in CPU, with speedups of up to 4.50x and 1.43x on average. Usingthe GPU algorithm, the experiments were able to speedup the original CPUalgorithms by up to 577x using an Nvidia Geforce GTX 980 Ti.

Bitmap Filter: Speeding up Exact Set Similarity Joins with Bitwise Operations