Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions

Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

Volumn , Issue , 2006, Pages 459-468

  Andoni, Alexandr ^a   Indyk, Piotr ^a  

^a Dept of Aeronautics and Astronautics

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDED-DISTANCE DECODERS; HASHING ALGORITHMS; LEECH LATTICE; NEAREST NEIGHBOR PROBLEM;

DECODING; PROBLEM SOLVING; QUERY PROCESSING;

APPROXIMATION ALGORITHMS;

EID: 38749118638     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FOCS.2006.49     Document Type: Conference Paper

References (32)

1. N. Ailon and B. Chazelle. Approximate nearest neighbors and the fast johnson-lindenstrauss transform. Proceedings of the Symposium on Theory of Computing, 2006.
2. O. Amrani and Y. Be'ery. Efficient bounded-distance decoding of the hexacode and associated decoders for the leech lattice and the golay code. IEEE Transactions on Communications, 44:534-537, May 1996.
3. O. Amrani, Y. Be'ery, A. Vardy, F.-W. Sun, and H. C. A. van Tilborg. The leech lattice and the golay code: Bounded-distance decoding and multilevel constructions. IEEE Transactions on Information Theory, 40:1030-1043, July 1994.
4. A. Andoni, M. Datar, N. Immorlica, P. Indyk, and V. Mirrokni. Locality-sensitive hashing scheme based on p-stable distributions. Nearest Neighbor Methods for Learning and Vision, Neural Processing Information Series, MIT Press, 2005.
5. A. Andoni and P. Indyk. E2lsh: Exact euclidean locality-sensitive hashing. Implementation available at http://web.mit.edu/andoni/www/LSH/ index.html, 2004.
6. A. Andoni, P. Indyk, and M. Pǎtraşcu. On the optimality of the dimensionality reduction method. Manuscript, 2006.
7. S. Arya, D. Mount, N. Netanyahu, R. Silverman, and A. Wu. An optimal algorithm for approximate nearest neighbor searching. Proceedings of the Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 573-582, 1994.
8. A. Chakrabarti and O. Regev. An optimal randomised cell probe lower bounds for approximate nearest neighbor searching. Proceedings of the Symposium on Foundations of Computer Science, 2004.
9. M. Charikar, C. Chekuri, A. Goel, S. Guha, and S. Plotkin. Approximating a finite metric by a small number of tree metrics. Proceedings of the Symposium on Foundations of Computer Science, 1998.
10. J. H. Conway and J. A. Sloane. Soft decoding techniques for codes and lattices, including the golay code and the leech lattice. IEEE Trans. Inf. Theor., 32(1):41-50, 1986.
11. J. H. Conway and J. A. Sloane. Sphere Packings, Lattices, and Groups. Springer-Verlag, New York, 1993.
12. M. Datar, N. Immorlica, P. Indyk, and V. Mirrokni. Locality-sensitive hashing scheme based on p-stable distributions. Proceedings of the ACM Symposium on Computational Geometry, 2004.
13. U. Feige and G. Schechtman. On the optimality of the random hyperplane rounding technique for max cut. Random Struct. Algorithms, 20(3):403-440, 2002.
14. G. Forney and A. Vardy. Generalized minimum distance decoding of euclidean-space codes and lattices. IEEE Transactions on Information Theory, 42:1992-2026, November 1996.
15. A. Gionis, P. Indyk, and R. Motwani. Similarity search in high dimensions via hashing. Proceedings of the 25th International Conference on Very Large Data Bases (VLDB), 1999.
16. S. Har-Peled. A replacement for voronoi diagrams of near linear size. Proceedings of the Symposium on Foundations of Computer Science, 2001.
17. S. Har-Peled and S. Mazumdar. Coresets for k-means and k-medians and their applications. Proceedings of the Symposium on Theory of Computing, 2004.
18. P. Indyk. High-dimensional computational geometry. Department of Computer Science, Stanford University, 2001.
19. P. Indyk. Approximate algorithms for high-dimensional geometric problems. Invited talk at DIMACS Workshop on Computational Geometry. Available at http://theory.csail.mit.edu/~indyk/high.ps, 2002.
20. P. Indyk. Better algorithms for high-dimensional proximity problems via asymmetric embeddings. Proceedings of the ACM-SIAM Symposium on Discrete Algorithms, 2003.
21. P. Indyk and R. Motwani. Approximate nearest neighbor: towards removing the curse of dimensionality. Proceedings of the Symposium on Theory of Computing, 1998.
22. D. Karger, R. Motwani, and M. Sudan. Approximate graph coloring by semidefinite programming. Proceedings of the 35th IEEE Symposium on Foundations of Computer Science, pages 2-13, 1994.
23. J. Kleinberg. Two algorithms for nearest-neighbor search in high dimensions. Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, 1997.
24. R. Krauthgamer and J. R. Lee. Navigating nets: Simple algorithms for proximity search. Proceedings of the ACM-SIAM Symposium on Discrete Algorithms, 2004.
25. E. Kushilevitz, R. Ostrovsky, and Y. Rabani. Efficient search for approximate nearest neighbor in high dimensional spaces. Proceedings of the Thirtieth ACM Symposium on Theory of Computing, pages 614-623, 1998.
26. J. Leech. Notes on sphere packings. Canadian Journal of Mathematics, 1967.
27. R. Motwani, A. Naor, and R. Panigrahy. Lower bounds on locality sensitive hashing. Proceedings of the ACM Symposium on Computational Geometry, 2006.
28. R. Panigrahy. Entropy-based nearest neighbor algorithm in high dimensions. Proceedings of the ACM-SIAM Symposium on Discrete Algorithms, 2006.
29. G. Pisier. The volume of convex bodies and Banach space geometry. Cambridge University Press, 1989.
30. H. Samet. Foundations of Multidimensional and Metric Data Structures. Elsevier, 2006.
31. G. Shakhnarovich, T. Darrell, and P. Indyk, editors. Nearest Neighbor Methods in Learning and Vision. Neural Processing Information Series, MIT Press, 2006.
32. A. Vardy and Y. Be'ery. Maximum-likelihood decoding of the leech lattice. IEEE Transactions on Information Theory, 39:1435-1444, July 1993.