Optimal hash functions for approximate closest pairs on the n-cube

TL;DR

This paper explores alternative hash functions for approximate closest pair detection on the n-cube, showing that decoding algorithms for codes outperform simple projections, especially asymptotically.

Contribution

It introduces decoding-based hash functions as superior alternatives to projection for approximate closest pair problems on the n-cube.

Findings

Decoding algorithms for codes outperform projections in certain parameters.

Asymptotically, random codes provide better hash functions than projections.

Decoding-based hash functions improve efficiency in nearest neighbor searches.

Abstract

One way to find closest pairs in large datasets is to use hash functions. In recent years locality-sensitive hash functions for various metrics have been given: projecting an n-cube onto k bits is simple hash function that performs well. In this paper we investigate alternatives to projection. For various parameters hash functions given by complete decoding algorithms for codes work better, and asymptotically random codes perform better than projection.