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.

翻译：通用L_p度量下的近似最近邻搜索（ANNS-U-L_p）是一个重要且富有挑战性的研究问题，因为它要求在不针对每个可能的p值构建索引的情况下，同时回答所有可能的p（0 < p ≤ 2）值下的查询。现有最优方法MLSH是一种基于局部敏感哈希（LSH）的ANNS方法，其查询性能勉强可接受。相比之下，基于图的ANNS方法在ANNS-L_p问题（固定p值）上可显著提升查询效率，但不能直接推广到ANNS-U-L_p问题。本文提出U-HNSW，这是首个针对ANNS-U-L_p的基于图的方法。我们的方案利用基于两种基度量（L_1和L_2）构建的HNSW图索引来生成有希望的最近邻候选点，然后通过早期终止策略验证这些候选点，大幅减少昂贵L_p距离计算的次数。实验结果表明，U-HNSW不仅在RAM磁盘上运行的原始MLSH实现相比，查询时间缩短高达2670倍（与理想化MLSH相比缩短高达15倍），而且在ANNS-L_p问题（固定p值）上，除少数特殊p值外，其性能也优于原始HNSW。