New LSH-based Algorithm for Approximate Nearest Neighbor

We present an algorithm for c-approximate nearest neighbor problem in a d-dimensional Euclidean space, achieving query time of O(dn1/c 2+o(1)) and space O(dn+n1+1/c 2+o(1)).

[1]  Sudipto Guha,et al.  Approximating a finite metric by a small number of tree metrics , 1998, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280).

[2]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

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

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

[5]  Nicole Immorlica,et al.  Locality-sensitive hashing scheme based on p-stable distributions , 2004, SCG '04.

[6]  Jon M. Kleinberg,et al.  Two algorithms for nearest-neighbor search in high dimensions , 1997, STOC '97.

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

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

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

[10]  Piotr Indyk,et al.  Similarity Search in High Dimensions via Hashing , 1999, VLDB.

[11]  Piotr Indyk,et al.  Better algorithms for high-dimensional proximity problems via asymmetric embeddings , 2003, SODA '03.

[12]  Rina Panigrahy,et al.  Entropy based nearest neighbor search in high dimensions , 2005, SODA '06.

[13]  G. Pisier.  The volume of convex bodies and Banach space geometry , 1989 .

[14]  Hans-Jörg Schek,et al.  A Quantitative Analysis and Performance Study for Similarity-Search Methods in High-Dimensional Spaces , 1998, VLDB.