Probabilistic behavior of hash tables

TL;DR

This paper extends previous work on hash function collision probabilities, demonstrating that under certain load conditions, the estimator's tail behavior is Gaussian, which improves understanding of hash table performance.

Contribution

It proves that the collision probability estimator has a Gaussian tail when the load factor exceeds a certain threshold, extending prior polynomial tail results.

Findings

Estimator exhibits Gaussian tail under high load

Provides upper bound for average search time in hashing with chaining

Applicable to user-specific key distributions

Abstract

We extend a result of Goldreich and Ron about estimating the collision probability of a hash function. Their estimate has a polynomial tail. We prove that when the load factor is greater than a certain constant, the estimator has a gaussian tail. As an application we find an estimate of an upper bound for the average search time in hashing with chaining, for a particular user (we allow the overall key distribution to be different from the key distribution of a particular user). The estimator has a gaussian tail.