Also quite recent are Ribbon filters: https://arxiv.org/abs/2103.02515 https://arxiv.org/abs/2103.02515 But these, and xor/binary-fuse-filters are only direct

Also quite recent are Ribbon filters: https://arxiv.org/abs/2103.02515 https://arxiv.org/abs/2103.02515 But these, and xor/binary-fuse-filters are only direct replacements for Bloom filters in some problems. There are still problems for which Bloom filters are a better solution. Bloom filters have the advantage that the filter produced by adding two elements, is the same as the bitwise-or of a pair of filters made by adding each element separately. bloom([x, y]) == bloom([x]) | bloom([y]) Also, the filter produced by bitwise-and, `bloom([x]) & bloom([y])`, cannot have any bits set in it which are not also set by `bloom([x, y])`. We can assert that bloom([x]) & bloom([x, y]) == bloom([x]) bloom([y]) & bloom([x, y]) == bloom([y]) (bloom([x]) & bloom([y])) | bloom([x, y]) == bloom([x, y]) There are practical applications that this can provide which are not satisfied by the "optimized" variants. The bitwise-or does set union (or least upper bound), and the bitwise-and does a set intersection (or greatest lower bound), though the filter produced by `bloom([x, y])` has a higher false positive rate than the filter produced by `bloom([x]) & bloom([y])`. bloom([x]) | bloom([y]) == bloom([x, y]) 🡥 🡤 bloom([x]) bloom([y]) 🡤 🡥 bloom([x]) & bloom([y])