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DOI: 10.4230/LIPIcs.ESA.2017.4
URN: urn:nbn:de:0030-drops-78182
URL: http://drops.dagstuhl.de/opus/volltexte/2017/7818/
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Agarwal, Pankaj K. ; Rubin, Natan ; Sharir, Micha

Approximate Nearest Neighbor Search Amid Higher-Dimensional Flats

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LIPIcs-ESA-2017-4.pdf (0.5 MB)


Abstract

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 k<d, and where, for each query point q, we want to return an input flat whose distance from q is at most (1 + epsilon) times the shortest such distance, where epsilon > 0 is another prespecified parameter. We present an algorithm that achieves this task with n^{k+1}(log(n)/epsilon)^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 near-quadratic storage to answer ANN queries amidst 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 amidst 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.

BibTeX - Entry

@InProceedings{agarwal_et_al:LIPIcs:2017:7818,
  author =	{Pankaj K. Agarwal and Natan Rubin and Micha Sharir},
  title =	{{Approximate Nearest Neighbor Search Amid Higher-Dimensional Flats}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{4:1--4:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Kirk Pruhs and Christian Sohler},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7818},
  URN =		{urn:nbn:de:0030-drops-78182},
  doi =		{10.4230/LIPIcs.ESA.2017.4},
  annote =	{Keywords: Approximate nearest neighbor search, k-flats, Polyhedral distance functions, Linear programming queries}
}

Keywords: Approximate nearest neighbor search, k-flats, Polyhedral distance functions, Linear programming queries
Seminar: 25th Annual European Symposium on Algorithms (ESA 2017)
Issue Date: 2017
Date of publication: 31.08.2017


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