Approximate nearest neighbor search for $\ell_p$-spaces ($2 < p < \infty$) via embeddings

TL;DR

This paper introduces the first non-trivial algorithms for approximate nearest neighbor search in $\, ext{l}_p$-spaces with $2 < p < \, extinfty$, filling a significant gap in high-dimensional similarity search methods.

Contribution

It develops novel algorithms with approximation guarantees for $\, extinfty$-norm spaces, expanding the scope of efficient nearest neighbor search beyond Euclidean and $\, extinfty$ spaces.

Findings

First algorithms with approximation guarantees for $\, extinfty$-norm spaces.

New embedding techniques for $\, extinfty$-spaces.

Improved theoretical understanding of $\, extinfty$-space search complexity.

Abstract

While the problem of approximate nearest neighbor search has been well-studied for Euclidean space and $\ell_1$, few non-trivial algorithms are known for $\ell_p$ when ($2 < p < \infty$). In this paper, we revisit this fundamental problem and present approximate nearest-neighbor search algorithms which give the first non-trivial approximation factor guarantees in this setting.