Graph-Based Nearest-Neighbor Search without the Spread

TL;DR

This paper presents a new graph-based data structure for approximate nearest-neighbor search that operates efficiently without depending on the spread of the data, achieving logarithmic query time in the number of points.

Contribution

It introduces a method to construct an external linear-size data structure that enables fast ANN queries independent of data spread.

Findings

Achieves logarithmic query time in n without spread dependence

Constructs a linear-size external data structure for ANN

Removes the unbounded spread limitation in nearest-neighbor graphs

Abstract

$\renewcommand{\Re}{\mathbb{R}}$Recent work showed how to construct nearest-neighbor graphs of linear size, on a given set $P$ of $n$ points in $\Re^d$, such that one can answer approximate nearest-neighbor queries in logarithmic time in the spread. Unfortunately, the spread might be unbounded in $n$, and an interesting theoretical question is how to remove the dependency on the spread. Here, we show how to construct an external linear-size data structure that, combined with the linear-size graph, allows us to answer ANN queries in logarithmic time in $n$.