Year: 2018
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Aamand, Anders, Thorup, Mikkel
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4289360747