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While the problem of approximate nearest neighbor search has been well-studied for Euclidean space and $\ell_1$, few non-trivial algorithms are known for $\ell_p$ when ($2 < p < \infty$).
Adaptive control processes: a guided tour
R. E. Bellman · 1961
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Embedding l p m l_{p}^{m} into l 1 n l_{1}^{n}
W.B. Johnson and G. Schechtman · 1982
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Extensions of Lipschitz mappings into a Hilbert space
W.B. Johnson and J. Lindenstrauss · 1984
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A randomized algorithm for closest-point queries
Kenneth L. Clarkson · 1988
Earlier work this paper cites.
l p l_{p} -spaces in data analysis
B. Fichet · 1988
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Isometric embedding in l p l_{p} -spaces
K. Ball · 1990
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Approximate closest-point queries in high dimensions
Marshall Bern · 1993
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Nearest neighbor queries in metric spaces
Kenneth L. Clarkson · 1997
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Approximate nearest neighbor queries revisited
T. M. Chan · 1998
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On approximate nearest neighbors in non-euclidean spaces
P. Indyk · 1998
Earlier work this paper cites.
Approximate nearest neighbors: Towards removing the curse of dimensionality
P. Indyk and R. Motwani · 1998
Earlier work this paper cites.
Efficient search for approximate nearest neighbor in high dimensional spaces
E. Kushilevitz, R. Ostrovsky, and Y. Rabani · 1998
Earlier work this paper cites.
Geometric Nonlinear Functional Analysis
Y. Binyamini and J. Lindenstrauss · 2000
Earlier work this paper cites.
Polynomial time approximation schemes for geometric k-clustering
R. Ostrovsky and Y. Rabani · 2000
Cited alongside, same era.
Searching in metric spaces
Edgar Chávez, Gonzalo Navarro, Ricardo Baeza-Yates, and José Luis Marroquín · 2001
Cited alongside, same era.
Algorithmic applications of low-distortion geometric embeddings
P. Indyk · 2001
Cited alongside, same era.
Linear-size approximate Voronoi diagrams
Sunil Arya and Theocharis Malamatos · 2002
Cited alongside, same era.
Finding nearest neighbors in growth-restricted metrics
David R. Karger and Matthias Ruhl · 2002
Cited alongside, same era.
Polynomial-time approximation schemes for geometric min-sum median clustering
R. Ostrovsky and Y. Rabani · 2002
Cited alongside, same era.
On approximate nearest neighbor search in ℓ p \ell_{p} , p > 2 p>2
Assaf Naor and Yuval Rabani · 2006
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Nearest-neighbor-preserving embeddings
P. Indyk and A. Naor · 2007
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Norm, point, and distance estimation over multiple signals using max-stable distributions
S.A. Stoev, M. Hadjieleftheriou, G. Kollios, and M.S. Taqqu · 2007
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Hardness of nearest neighbor under l-infinity
A. Andoni, D. Croitoru, and M. Patrascu · 2008
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A locality-sensitive hash for real vectors
Tyler Neylon · 2010
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Low distortion metric embedding into constant dimension
András Faragó · 2011
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Shades of gray and colour constancy
Graham D. Finlayson and Elisabetta Trezzi · 2004
Cited alongside, same era.
Navigating nets: Simple algorithms for proximity search
R. Krauthgamer and J.R. Lee · 2004
Cited alongside, same era.
Approximate nearest neighbors and the fast Johnson-Lindenstrauss transform
N. Ailon and B. Chazelle · 2006
Cited alongside, same era.
Oblivious string embeddings and edit distance approximations
T. Batu, F. Ergun, and C. Sahinalp · 2006
Cited alongside, same era.
Cover trees for nearest neighbor
Alina Beygelzimer, Sham Kakade, and John Langford · 2006
Cited alongside, same era.
Searching dynamic point sets in spaces with bounded doubling dimension
R. Cole and L. Gottlieb · 2006
Cited alongside, same era.
General l p l_{p} constrained approach for colour constancy
G.D. Finlayson, P.A.T. Rey, and E. Trezzi · 2011
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Making the nearest neighbor meaningful for time series classification
Daren Yu, Xiao Yu, and Anqi Wu · 2011
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Minkowski metric, feature weighting and anomalous cluster initializing in k-means clustering
Renato Cordeiro de Amorim and Boris Mirkin · 2012
Later among the works it cites.
Approximate nearest neighbors: Towards removing the curse of dimensionality
S. Har-Peled, P. Indyk, and R. Motwani · 2012
Later among the works it cites.
High frequency moments via max-stability
A. Andoni · 2013
Later among the works it cites.
Comparison of metric spectral gaps
Assaf Naor · 2014
Later among the works it cites.
Approximating minimization diagrams and generalized proximity search
Sariel Har-Peled and Nirman Kumar · 2015
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