Linear Probing with 5-Independent Hashing

TL;DR

This paper demonstrates that linear probing hash tables achieve expected constant time operations when using 5-independent hash functions, with simplified proofs and extensions to space-efficient variants with false positives.

Contribution

Provides a simplified proof that linear probing with 5-independent hashing has expected constant time, and explores a space-efficient variant with false positives.

Findings

Linear probing with 5-independent hashing has expected constant time.

A smaller space version of linear probing can have false positives.

The use of higher moments in analyzing data structures is illustrated.

Abstract

These lecture notes show that linear probing takes expected constant time if the hash function is 5-independent. This result was first proved by Pagh et al. [STOC'07,SICOMP'09]. The simple proof here is essentially taken from [Patrascu and Thorup ICALP'10]. We will also consider a smaller space version of linear probing that may have false positives like Bloom filters. These lecture notes illustrate the use of higher moments in data structures, and could be used in a course on randomized algorithms.