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AHash: A Load-Balanced One Permutation Hash

Minwise Hashing (MinHash) is a fundamental method to compute set similarities and compact high-dimensional data for efficient learning and searching. The bottleneck of MinHash is computing k (usually hundreds) MinHash values. One Permutation Hashing (OPH) only requires one permutation (hash function) to get k MinHash values by dividing elements into k bins. One drawback of OPH is that the load of the bins (the number of elements in a bin) could be unbalanced, which leads to the existence of empty bins and false similarity computation. Several strategies for densification, that is, filling empty bins, have been proposed. However, the densification is just a remedial strategy and cannot eliminate the error incurred by the unbalanced load. Unlike the densification to fill the empty bins after they undesirably occur, our design goal is to balance the load so as to reduce the empty bins in advance. In this paper, we propose a load-balanced hashing, Amortization Hashing (AHash), which can generate as few empty bins as possible. Therefore, AHash is more load-balanced and accurate without hurting runtime efficiency compared with OPH and densification strategies. Our experiments on real datasets validate the claim. All source codes and datasets have been provided as Supplementary Materials and released on GitHub anonymously.

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