Perfect and separating Hash families: new bounds via the algorithmic cluster expansion local lemma

TL;DR

This paper introduces new lower bounds for perfect and separating hash families using an advanced algorithmic version of the Lovász Local Lemma, demonstrating polynomial-time constructibility via the Moser-Tardos algorithm.

Contribution

It provides novel bounds for hash families and shows their efficient construction through an improved algorithmic approach.

Findings

New lower bounds for hash families established.

Polynomial-time algorithms for constructing these hash families.

Enhanced theoretical understanding of hash family existence conditions.

Abstract

We present new lower bounds for the size of perfect and separating hash families ensuring their existence. Such new bounds are based on the algorithmic Cluster expansion improved version of the Lov\'asz Local Lemma, which also implies that the Moser-Tardos algorithm finds such hash families in polynomial time.