Weighted Bloom Filter

Abstract

A Bloom filter is a simple randomized data structure that answers membership query with no false negative and a small false positive probability. It is an elegant data compression technique for membership information and has broad applications. In this paper, we generalize the traditional Bloom filter to Weighted Bloom Filter, which incorporates the information on the query frequencies and the membership likelihood of the elements into its optimal design. It has been widely observed that in many applications, some popular elements are queried much more often than the others. The traditional Bloom filter for data sets with irregular query patterns and non-uniform membership likelihood can be further optimized. We derive the optimal configuration of the Bloom filter with query-frequency and membership-likelihood information, and show that the adapted Bloom filter always outperforms the traditional Bloom filter. Under reasonable frequency models such as the step distribution or the Zipf's distribution, the improvement of the false positive probability of the weighted Bloom filter over that of the traditional Bloom filter has been evaluated by simulations.