Approximate Nearest Neighbor Search for $$\ell _p$$-Spaces $$(2<p<\infty )$$ via Embeddings

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 best known approximation factor guarantees in this setting.