A Bloom filter was designed to be a data structure optimized for fast, space-efficient set membership tests. Bloom filters have the unusual property of requiring constant time to add an element to the set or test for membership, regardless of the size of the elements or the number of elements already in the set. No other constant-space set data structure has this property. It works by storing a bit vector representing the set S = {h[i](x) | x in S, i = 1, …, k}, where h[1], …, h[k] := {0, 1} -> [n lg(1/ε) lg e] are hash functions. Additions are simply setting k bits to 1, specifically those at h[1](x), …, h[k](x). Checks are implemented by performing those same hash functions and returning if all of the resulting positions are 1. Because the set stored is a proper superset of the set of items added, false positives may occur, though false negatives cannot. The false positive rate can be specified.A data structure optimized for fast, space-efficient set membership tests
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