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Among many solutions to the high-dimensional approximate nearest neighbor(ANN) search problem, locality sensitive hashing (LSH) is known for itssub-linear query time and robust theoretical guarantee on query accuracy.Traditional LSH methods can generate a small number of candidates quickly fromhash tables but suffer from large index sizes and hash boundary problems.Recent studies to address these issues often incur extra overhead to identifyeligible candidates or remove false positives, making query time no longersub-linear. To address this dilemma, in this paper we propose a novel LSHscheme called DB-LSH which supports efficient ANN search for largehigh-dimensional datasets. It organizes the projected spaces withmulti-dimensional indexes rather than using fixed-width hash buckets. Ourapproach can significantly reduce the space cost as by avoiding the need tomaintain many hash tables for different bucket sizes. During the query phase ofDB-LSH, a small number of high-quality candidates can be generated efficientlyby dynamically constructing query-based hypercubic buckets with the requiredwidths through index-based window queries. For a dataset of $n$ $d$-dimensionalpoints with approximation ratio $c$, our rigorous theoretical analysis showsthat DB-LSH achieves a smaller query cost ${O(n^{\rho^*} d\log n)}$, where${\rho^*}$ is bounded by ${1/c^{\alpha}}$ while the bound is ${1/c}$ in theexisting work. An extensive range of experiments on real-world datademonstrates the superiority of DB-LSH over state-of-the-art methods on bothefficiency and accuracy.

DB-LSH: Locality-Sensitive Hashing with Query-based Dynamic Bucketing