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

2026-05-03

AI Summary

This work addresses the challenge of enabling approximate nearest neighbor search under any $L_p$ metric for $0 < p \leq 2$ without constructing a separate index for each $p$ (ANNS-U-$L_p$) by proposing U-HNSW, the first graph-based method for this problem. U-HNSW constructs an HNSW graph using $L_1$ and $L_2$ metrics to generate candidate neighbors, then integrates an early termination strategy with efficient $L_p$ distance computation to drastically reduce costly distance evaluations. As the first approach to incorporate graph structures into universal $L_p$ metric ANNS, U-HNSW overcomes the efficiency limitations of traditional locality-sensitive hashing (LSH). It outperforms standard HNSW even in fixed-$p$ settings and achieves up to a 2,670× speedup over MLSH and a 15× speedup over an idealized MLSH baseline.

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.

Problem

• Approximate Nearest Neighbor Search
• Universal Lp Metrics
• ANNS-U-Lp
• Indexing
• Distance Computation

Innovation

• graph-based ANNS
• universal Lp metrics
• HNSW
• early-termination strategy
• approximate nearest neighbor search