A novel and precise false positive probability computation for Bloom Filters implemented with universal hash functions

Koltuk, Furkan
Bloom Filters (BF) are multiple-hashing data structures that are widely used in membership testing applications. The many-to-one nature of the BF hashing results in false positive outcomes which have to be further processed at a performance cost. The computation of the false positive probability of BFs is carried out under the assumption of uniform and independent hash functions. To the best of our knowledge, all previous work in the literature assume that the hash functions are uniform and independent without verifying if that is the case in reality. This thesis focuses on the hash function uniformity and independence for BFs with universal H3 functions. To this end, we propose a formal framework for defining and quantifying the uniformity and independence for H3 hash functions in BFs. Furthermore, we define a formal description of the many-to-one outcomes of H3 hash functions. We then use this framework to precisely compute the false positive probability for BFs with H3 hash functions which might not be necessarily uniform or independent. We verify our precise false positive expression with a hardware test bed that can execute 2 · 10^8 membership queries per second. We perform structured tests to evaluate the effect of losing uniformity and independence at different levels among the H3 hash functions. Furthermore, we evaluate the results of our expression for a range of parameters.


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Citation Formats
F. Koltuk, “A novel and precise false positive probability computation for Bloom Filters implemented with universal hash functions,” M.S. - Master of Science, Middle East Technical University, 2022.