Another Proof of Cuckoo hashing with New Variants

TL;DR

This paper presents a simpler proof for the load capacity of Cuckoo Hashing, enabling easier understanding and potential generalizations, originally derived in a privacy protocol context.

Contribution

It introduces a new, more accessible proof for Cuckoo Hashing load bounds, facilitating further research and extensions.

Findings

Simpler proof for Cuckoo Hashing load capacity

Original proof from Pinkas et al. adapted for clarity

Potential for new generalizations in hashing algorithms

Abstract

We show a new proof for the load of obtained by a Cuckoo Hashing data structure. Our proof is arguably simpler than previous proofs and allows for new generalizations. The proof first appeared in Pinkas et. al. \cite{PSWW19} in the context of a protocol for private set intersection. We present it here separately to improve its readability.