Explicit and Efficient Hash Families Suffice for Cuckoo Hashing with a Stash

TL;DR

This paper demonstrates that simple, explicit hash families with limited independence are sufficient for cuckoo hashing with a stash, maintaining strong performance guarantees and simplifying analysis.

Contribution

It introduces the use of 2-wise independent hash families for cuckoo hashing with a stash, reducing complexity while preserving performance guarantees.

Findings

Rehash probability is O(1/n^{s+1}) with stash size s

Evaluation time is O(s)

Simple hash families suffice for effective cuckoo hashing

Abstract

It is shown that for cuckoo hashing with a stash as proposed by Kirsch, Mitzenmacher, and Wieder (2008) families of very simple hash functions can be used, maintaining the favorable performance guarantees: with stash size $s$ the probability of a rehash is $O(1/n^{s+1})$, and the evaluation time is $O(s)$. Instead of the full randomness needed for the analysis of Kirsch et al. and of Kutzelnigg (2010) (resp. $\Theta(\log n)$-wise independence for standard cuckoo hashing) the new approach even works with 2-wise independent hash families as building blocks. Both construction and analysis build upon the work of Dietzfelbinger and Woelfel (2003). The analysis, which can also be applied to the fully random case, utilizes a graph counting argument and is much simpler than previous proofs. As a byproduct, an algorithm for simulating uniform hashing is obtained. While it requires about twice as much space as the most space efficient solutions, it is attractive because of its simple and direct structure.