Maximum Bipartite Matching Size And Application to Cuckoo Hashing

TL;DR

This paper analyzes the maximum bipartite matching size in random graphs to understand and improve cuckoo hashing with a stash, especially at high memory loads, providing exact and asymptotic results.

Contribution

It offers the first detailed analysis of maximum bipartite matching size for high load cuckoo hashing, including exact finite and asymptotic results, and applies findings to real network data.

Findings

Provides exact formulas for maximum matching size at finite system sizes.

Derives asymptotic bounds as system size grows.

Establishes a tight lower bound on stash size for multiple-choice hashing.

Abstract

Cuckoo hashing with a stash is a robust multiple choice hashing scheme with high memory utilization that can be used in many network device applications. Unfortunately, for memory loads beyond 0.5, little is known on its performance. In this paper, we analyze its average performance over such loads. We tackle this problem by recasting the problem as an analysis of the expected maximum matching size of a given random bipartite graph. We provide exact results for any finite system, and also deduce asymptotic results as the memory size increases. We further consider other variants of this problem, and finally evaluate the performance of our models on Internet backbone traces. More generally, our results give a tight lower bound on the size of the stash needed for any multiple-choice hashing scheme.