18.415 Project - Using a Count-Min sketch structure for easier analysis of Bloom filter false positive rates

The classical proof for Bloom filter false positive rates was shown to be incorrect due to a subtle error regarding independence of events. Although the previously computed false positive rate is asymptotically still correct, it is incorrect for small parameter values and is generally only a lower bound [BGK08]. Indeed, the correct analysis for Bloom filters does not admit a convenient closed form, though efficient computations do exist [CRJ10]. In this paper, we outline the strategy of the new analysis Furthermore, we demonstrate that for large parameter values, we can use a Count-Min [CM05] data structure to asymptotically recover a classical Bloom filter false positive rate using only the naive analysis scheme. This has no practical applications, as the Bloom filter is strictly better in every sense, but this construction may be useful pedagogically in demonstrating the subtleties involved when working with independence. Lastly, exact expected false positive rates are trivially computable for this structure; though the rates are worse than for regular Bloom filters, this might somehow be useful theoretically.