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We study the $r$-near neighbors reporting problem ($r$-NN), i.e., reporting\emph{all} points in a high-dimensional point set $S$ that lie within a radius$r$ of a given query point $q$. Our approach builds upon on thelocality-sensitive hashing (LSH) framework due to its appealing asymptoticsublinear query time for near neighbor search problems in high-dimensionalspace. A bottleneck of the traditional LSH scheme for solving $r$-NN is thatits performance is sensitive to data and query-dependent parameters. Ondatasets whose data distributions have diverse local density patterns, LSH withinappropriate tuning parameters can sometimes be outperformed by a simplelinear search.  In this paper, we introduce a hybrid search strategy between LSH-based searchand linear search for $r$-NN in high-dimensional space. By integrating anauxiliary data structure into LSH hash tables, we can efficiently estimate thecomputational cost of LSH-based search for a given query regardless of the datadistribution. This means that we are able to choose the appropriate searchstrategy between LSH-based search and linear search to achieve betterperformance. Moreover, the integrated data structure is time efficient and fitswell with many recent state-of-the-art LSH-based approaches. Our experiments onreal-world datasets show that the hybrid search approach outperforms (or iscomparable to) both LSH-based search and linear search for a wide range ofsearch radii and data distributions in high-dimensional space.

Hybrid LSH: Faster Near Neighbors Reporting in High-dimensional Space