Non-empty Bins With Simple Tabulation Hashing
Anders Aamand, Mikkel Thorup . Arxiv 2018 – 0 citations
We consider the hashing of a set (X\subseteq U) with (|X|=m) using a simple tabulation hash function (h:U\to [n]=\{0,\dots,n-1\}) and analyse the number of non-empty bins, that is, the size of (h(X)). We show that the expected size of (h(X)) matches that with fully random hashing to within low-order terms. We also provide concentration bounds. The number of non-empty bins is a fundamental measure in the balls and bins paradigm, and it is critical in applications such as Bloom filters and Filter hashing. For example, normally Bloom filters are proportioned for a desired low false-positive probability assuming fully random hashing (see \url{en.wikipedia.org/wiki/Bloom_filter}). Our results imply that if we implement the hashing with simple tabulation, we obtain the same low false-positive probability for any possible input.