Balanced Allocations and Double Hashing

TL;DR

This paper investigates the effectiveness of double hashing in balanced allocation schemes, showing empirically that it performs nearly as well as fully random hashing and providing theoretical explanations for this behavior.

Contribution

It offers the first empirical and theoretical analysis demonstrating that double hashing is nearly as effective as fully random hashing in balanced allocation problems.

Findings

Double hashing performs similarly to fully random hashing in balanced allocation.

Empirical results show negligible performance difference between the two methods.

Theoretical analysis explains why double hashing is effective in this context.

Abstract

Double hashing has recently found more common usage in schemes that use multiple hash functions. In double hashing, for an item $x$, one generates two hash values $f(x)$ and $g(x)$, and then uses combinations $(f(x) +k g(x)) \bmod n$ for $k=0,1,2,...$ to generate multiple hash values from the initial two. We first perform an empirical study showing that, surprisingly, the performance difference between double hashing and fully random hashing appears negligible in the standard balanced allocation paradigm, where each item is placed in the least loaded of $d$ choices, as well as several related variants. We then provide theoretical results that explain the behavior of double hashing in this context.