Universal hashing in VLSI

Abstract

A problem is presented with deterministic VLSI complexity AT ² _det =Ω(N²), but Las Vegas complexity only AT ²_{Las Vegas} =O (N poly(logN)). (The Las Vegas algorithm always decides correctly, but T is only the expected running time; A is the area of the chip). Previously AT ²_{Las Vegas} =O(N^3/2 poly(logN)) has been shown for a similar problem with a more complicated algorithm. Here, we use a simple universal hashing technique based on random linear functions. We hope this will give rise to other applications of universal hashing in VLSI.

Our algorithm is very practical, because the random bits can even be wired into the chip. For every sequence of inputs during a chip's lifetime, the chances are high that the same short random bit string will always produce the result quickly.