Simple minimal perfect hashing in less space

Abstract

A minimal perfect hash function for a set S is an injective mapping from S to {0,. .., |S|−1}. Taking as our model of computation a unit-cost RAM with a word length of w bits, we consider the problem of constructing minimal perfect hash functions with constant evaluation time for arbitrary subsets of U = {0,. .. . 2w – 1}. Pagh recently described a simple randomized algorithm that, given a set S ⊆ U of size n, works in O(n) expected time and computes a minimal perfect hash function for S whose representation, besides a constant number of words, is a table of at most (2+ ϵ)n integers in the range {0,. .., n−1}, for arbitrary fixed ϵ > 0. Extending his method, we show how to replace the factor of 2 + ϵ by 1 + ϵ.