Approximate nearest neighbor search amid higher-dimensional flats

Pankaj K. Agarwal, Natan Rubin, Micha Sharir

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We consider the approximate nearest neighbor (ANN) problem where the input set consists of n k-flats in the Euclidean Rd, for any fixed parameters 0 ≤ k < d, and where, for each query point q, we want to return an input flat whose distance from q is at most (1 + ϵ) times the shortest such distance, where ϵ > 0 is another prespecified parameter. We present an algorithm that achieves this task with nk+1(log(n)/ ϵ)O(1) storage and preprocessing (where the constant of proportionality in the big-O notation depends on d), and can answer a query in O(polylog(n)) time (where the power of the logarithm depends on d and k). In particular, we need only nearquadratic storage to answer ANN queries amid a set of n lines in any fixed-dimensional Euclidean space. As a by-product, our approach also yields an algorithm, with similar performance bounds, for answering exact nearest neighbor queries amid k-flats with respect to any polyhedral distance function. Our results are more general, in that they also provide a tradeoff between storage and query time.

Original languageAmerican English
Title of host publication25th European Symposium on Algorithms, ESA 2017
EditorsChristian Sohler, Kirk Pruhs
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770491
StatePublished - 1 Sep 2017
Event25th European Symposium on Algorithms, ESA 2017 - Vienna, Austria
Duration: 4 Sep 20176 Sep 2017

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs


Conference25th European Symposium on Algorithms, ESA 2017


  • Approximate nearest neighbor search
  • K-flats
  • Linear programming queries
  • Polyhedral distance functions

All Science Journal Classification (ASJC) codes

  • Software


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