Fast Construction of Nets in Low Dimensional Metrics, and Their Applications

TL;DR

This paper introduces a near-linear time algorithm for building hierarchical nets in low-dimensional metric spaces, enabling faster solutions for various geometric and data analysis problems.

Contribution

It provides the first near-linear time construction of hierarchical nets in low-dimensional metrics, improving efficiency for multiple applications.

Findings

Near-linear preprocessing time for hierarchical nets

Linear space usage in applications

Improved algorithms for nearest neighbor and related problems

Abstract

We present a near linear time algorithm for constructing hierarchical nets in finite metric spaces with constant doubling dimension. This data-structure is then applied to obtain improved algorithms for the following problems: Approximate nearest neighbor search, well-separated pair decomposition, compact representation scheme, doubling measure, and computation of the (approximate) Lipschitz constant of a function. In all cases, the running (preprocessing) time is near-linear and the space being used is linear.