Approximate nearest neighbor search for low dimensional queries

We study the Approximate Nearest Neighbor problem for metric spaces where the query points are constrained to lie on a subspace of low doubling dimension.

[1]  Alexandr Andoni,et al.  Near-Optimal Hashing Algorithms for Approximate Nearest Neighbor in High Dimensions , 2006, 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06).

[2]  K. Clarkson Nearest-Neighbor Searching and Metric Space Dimensions , 2005 .

[3]  Rafail Ostrovsky,et al.  Efficient search for approximate nearest neighbor in high dimensional spaces , 1998, STOC '98.

[4]  Jirí Matousek,et al.  Ray shooting and parametric search , 1992, STOC '92.

[5]  Sunil Arya,et al.  An optimal algorithm for approximate nearest neighbor searching fixed dimensions , 1998, JACM.

[6]  Piotr Indyk,et al.  Nearest-neighbor-preserving embeddings , 2007, TALG.

[7]  Sunil Arya,et al.  Linear-size approximate voronoi diagrams , 2002, SODA '02.

[8]  Mark de Berg,et al.  Computational geometry: algorithms and applications , 1997 .

[9]  S. Meiser,et al.  Point Location in Arrangements of Hyperplanes , 1993, Inf. Comput..

[10]  David R. Karger,et al.  Finding nearest neighbors in growth-restricted metrics , 2002, STOC '02.

[11]  Sunil Arya,et al.  Space-time tradeoffs for approximate nearest neighbor searching , 2009, JACM.

[12]  S. Rao Kosaraju,et al.  A decomposition of multidimensional point sets with applications to k-nearest-neighbors and n-body potential fields , 1995, JACM.

[13]  W. B. Johnson,et al.  Extensions of Lipschitz mappings into Hilbert space , 1984 .

[14]  Sariel Har-Peled,et al.  Fast construction of nets in low dimensional metrics, and their applications , 2004, SCG.

[15]  Sariel Har-Peled Geometric Approximation Algorithms , 2011 .

[16]  P. Assouad Plongements lipschitziens dans Rn , 2003 .

[17]  Robert Krauthgamer,et al.  Navigating nets: simple algorithms for proximity search , 2004, SODA '04.

[18]  Piotr Indyk,et al.  Approximate nearest neighbors: towards removing the curse of dimensionality , 1998, STOC '98.

[19]  Sariel Har-Peled A replacement for Voronoi diagrams of near linear size , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[20]  Satish Rao,et al.  A note on the nearest neighbor in growth-restricted metrics , 2004, SODA '04.

[21]  Rajeev Motwani,et al.  Lower bounds on locality sensitive hashing , 2005, SCG '06.

[22]  Robert Krauthgamer,et al.  Bounded geometries, fractals, and low-distortion embeddings , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

[23]  Kenneth L. Clarkson,et al.  A Randomized Algorithm for Closest-Point Queries , 1988, SIAM J. Comput..

[24]  J. Heinonen Lectures on Analysis on Metric Spaces , 2000 .

[25]  Kunal Talwar,et al.  Bypassing the embedding: algorithms for low dimensional metrics , 2004, STOC '04.

[26]  Patrice Assouad Plongements lipschitziens dans ${\mathbb {R}}^n$ , 1983 .

[27]  Lee-Ad Gottlieb,et al.  A Nonlinear Approach to Dimension Reduction , 2009, SODA '11.