Partially Specified Nearest Neighbor Search

We study the Partial Nearest Neighbor Problem that consists in preprocessing n points D from d-dimensional metric space such that the following query can be answered efficiently: Given a query vector Q ∈ R and an axes-aligned query subspace represented by S ∈ {0, 1}, report a point P ∈ D with dS(Q,P ) ≤ dS(Q,P ′) for all P ′ ∈ D, where dS(Q,P ) is the distance between Q and P in the subspace S. This problem is related to similarity search between feature vectors w.r.t. a subset of features. Thus, the problem is of great practical importance in bioinformatics, image recognition, etc., however, due to exponentially many subspaces, each changing distances significantly, the problem has a considerable complexity. We present the first exact algorithms for `2and `∞-metrics with linear space and sub-linear worst-case query time. We also give a simple approximation algorithm, and show experimentally that our approach performs well on real world data.