Partially Specified Nearest Neighbor Search

  • Tomas Hruz
  • Marcel Schöngens
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7434)


We study the Partial Nearest Neighbor Problem that consists in preprocessing n points \(\mathcal{D}\) from d-dimensional metric space such that the following query can be answered efficiently: Given a query vector Q ∈ ℝ d and an axes-aligned query subspace represented by S ∈ {0,1} d , report a point \(P \in \mathcal{D}\) with d S (Q,P) ≤ d S (Q,P′) for all \(P' \in \mathcal{D}\), where d S (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 ℓ2- and ℓ ∞ -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.


Approximation Ratio Near Neighbor Query Range Query Point Query Time 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Tomas Hruz
    • 1
  • Marcel Schöngens
    • 1
  1. 1.Institute of Theoretical Computer ScienceETH ZurichSwitzerland

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