U-HNSW: An Efficient Graph-based Solution to ANNS Under Universal Lp Metrics

TL;DR

U-HNSW is a novel graph-based method that efficiently performs approximate nearest neighbor search across all p values in (0, 2], significantly outperforming existing solutions in speed.

Contribution

It introduces the first graph-based approach for universal L_p ANNS, combining HNSW graphs with an early-termination strategy for broad p-value applicability.

Findings

U-HNSW achieves up to 2670 times faster query times than MLSH.

Outperforms original HNSW on fixed p-value ANNS tasks for most p values.

Significantly reduces the number of expensive L_p distance computations.

Abstract

Approximate nearest neighbor search under universal L_p metrics (ANNS-U-L_p) is an important and challenging research problem, as it requires answering queries under all possible p (0<p <= 2) values simultaneously without building an index for each possible p value. The state-of-the-art solution, called MLSH, is a Locality-Sensitive Hashing (LSH)-based ANNS method with barely acceptable query performance. In contrast, graph-based ANNS methods, which offer significantly improved query efficiency on the ANNS-L_p problem (with a fixed p-value), cannot be naively extended to the ANNS-U-$L_p$ problem. In this paper, we propose U-HNSW, the first graph-based method for ANNS-U-L_p. Our scheme uses HNSW graph indexes built on two base metrics ($L_1$ and $L_2$) to generate promising nearest neighbors candidates, and then verifies these candidates with an early-termination strategy that substantially reduces the number of expensive L_p distance computations. Experimental results show that U-HNSW not only achieves up to 2670 times shorter query times than the original MLSH implementation running on a RAM disk (up to 15 times shorter than the idealized MLSH), but also outperforms the original HNSW on the ANNS-L_p problem (with a fixed p-value), except for a few special p values.