On the insertion time of random walk cuckoo hashing

TL;DR

This paper proves that with a sufficiently large constant number of hash functions, the expected insertion time in random walk cuckoo hashing is constant, resolving an open question about its efficiency.

Contribution

It establishes that for a sufficiently large constant number of hash functions, the expected insertion time in random walk cuckoo hashing is constant.

Findings

Expected insertion time is O(1) for sufficiently large constant d.

The result addresses an open question in cuckoo hashing efficiency.

The analysis applies when the number of hash functions d=O(1).

Abstract

Cuckoo Hashing is a hashing scheme invented by Pagh and Rodler. It uses $d\geq 2$ distinct hash functions to insert items into the hash table. It has been an open question for some time as to the expected time for Random Walk Insertion to add items. We show that if the number of hash functions $d=O(1)$ is sufficiently large, then the expected insertion time is $O(1)$ per item.