Tighter lower bounds for nearest neighbor search and related problems in the cell probe model

Journal of Computer and System Sciences

Volumn 64, Issue 4, 2002, Pages 873-896

  Barkol, Orner ^a   Rabani, Yuval ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; GRAPHIC METHODS; INTERPOLATION; MATHEMATICAL MODELS; OPTIMIZATION; POLYNOMIAL APPROXIMATION; PROBLEM SOLVING; QUERY LANGUAGES;

LOWER BOUNDS; POLYLOGS; SPANNING TREES; YAO'S CELL PROBE MODEL;

THEOREM PROVING;

EID: 23844444187     PISSN: 00220000     EISSN: 10902724     Source Type: Journal    
DOI: 10.1006/jcss.2002.1831     Document Type: Conference Paper

References (36)

1. P. K. Agarwal and J. Matoušek, Ray shooting and parametric search, in "Proc. of 24th STOC," pp. 517-526, 1992.
2. M. Ajtai, Determinism versus non-determinism for linear-time RAMs, in "Proc. of 31st STOC," pp. 632-641, 1999.
3. M. Ajtai, A non-linear time lower bound for Boolean branching programs, preprint, April 1999.
4. N. Alon and J. Spencer, "The Probabilistic Method," Wiley, New York, 1992.
5. S. Arya and D. Mount, Approximate nearest neighbor searching, in "Proc. of 4th SODA," pp. 271-280, 1993.
6. S. Arya, D. Mount, N. Netanyahu, R. Silverman, and A. Wu, An optimal algorithm for approximate nearest neighbor searching in fixed dimensions, in "Proc. of 5th SODA," pp. 573-582, 1994.
7. P. Beame, M. Saks, and J. S. Thathachar, Time-space tradeoffs for branching programs, in "Proc. of 39th FOCS," pp. 254-263, 1998.
8. J. S. Beis and D. O. Lowe, Shape indexing using approximate nearest-neighbor search in high-dimensional spaces, in "Proc. IEEE Conf. Comp. Vision Patt. Recog.," pp. 1000-1006, 1997.
9. M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf, "Computational Geometry Algorithms and Applications," Springer-Verlag, Berlin, 1997.
10. A. Borodin, R. Ostrovsky, and Y. Rabani, Lower bounds for high dimensional nearest neighbor search and related problems, in "Proc. of 31th STOC," pp. 312-321, 1999.
11. A. Chakrabarti, B. Chazelle, B. Gum, and A. Lvov, A good neighbor is hard to find, in "Proc. of 31st STOC," pp. 305-311, 1999.
12. K. Clarkson, A randomized algorithm for closest-point queries, SIAM J. Camput. 17 (1988), 830-847.
13. A. Clarkson, An algorithm for approximate closest-point queries, in "Proc. of 10th SCO," pp. 160-164, 1994.
14. S. Cost and S. Salzberg, A weighted nearest neighbor algorithm for learning with symbolic features, Mach. Learning 10 (1993), 57-67.
15. T. M. Cover and P. E. Hart, Nearest neighbor pattern classification, IEEE-IT 13 (1967), 21-27.
16. S. Deerwester, S. T. Dumais, G. W. Furnas, T. K. Landauer, and R. Harshman, Indexing by latent semantic analysis, J. Amer. Soc. Info. Sci. 41 (1990), 391-407.
17. L. Devroye and T. J. Wagner, Nearest neighbor methods in discrimination, in "Handbook of Statistics" (P. R. Krishnaiah and L. N. Kanal, Eds.), Vol. 2, North-Holland, Amsterdam, 1982.
18. D. Dobkin and R. Lipton, Multidimensional search problems, SIAM J. Comput. 5 (1976), 181-186.
19. M. Flickner, H. Sawhney, W. Niblack, J. Ashley, Q. Huang, B. Dom, M. Gorkani, J. Hafner, D. Lee, D. Petkovic, D. Steele, and P. Yanker, Query by image and video content: The QBIC system, IEEE Comput. 28 (1995), 23-32.
20. R. O. Duda and P. E. Hart, "Pattern Classification and Scene Analysis," Wiley, New York, 1973.
21. R. Fagin, Fuzzy queries in multimedia database systems, in "Proc. of PODS," 1998.
22. A. Gersho and R. M. Gray, "Vector Quantization and Signal Compression," Kluwer Academic, Dordrecht, 1991.
23. T. Hastie and R. Tibshirani, Discriminant adaptive nearest neighbor classification, in " 1st International Conf. on Knowledge Discovery and Data Mining," 1995.
24. P. Indyk, Dimensionality reduction techniques for proximity problems, manuscript, Aug. 1999, to appear in SODA 2000.
25. P. Indyk and R. Motwani, Approximate nearest neighbors: Toward removing the curse of dimensionality, in "Proc. of 30th STOC," pp. 604-613, 1998.
26. J. Kleinberg, Two algorithms for nearest-neighbor search in high dimensions, in "Proc. of 29th STOC," pp. 599-608, 1997.
27. E. Kushilevitz, R. Ostrovsky, and Y. Rabani, Efficient search for approximate nearest neighbor in high dimensional spaces, in "Proc. of 30th STOC," pp. 614-623, 1998.
28. J. Matoušek, Reporting points in halfspaces, in "Proc. of 32nd FOCS," pp. 207-215, 1991.
29. S. Meiser, Point location in arrangements of hyperplanes, Inform. Comput. 106 (1993), 286-303.
30. P. B. Miltersen, Lower bounds for union-split-find related problems on random access machines, in "Proc. of 26th STOC," pp. 625-634, 1994.
31. P. B. Miltersen, N. Nisan, S. Safra, and A. Widgerson, On data-structures and asymmetric communication complexity, in "Proc. of 27th STOC," pp. 103-111, 1995.
32. A. Pentland, R. W. Picard, and S. Sclaroff, Photobook: tools for content-based manipulation of image databases, in "Proc. SPIE Conf. on Storage and Retrieval of Image and Video Databases II," 1994.
33. G. Salton, "Automatic Text Processing," Addison-Wesley, Reading, MA, 1989.
34. A. W. M. Smoulders and R. Jain (Eds.), "Proc. 1st Workshop on Image Databases and Multi-Media Search," 1996.
35. A. C. Yao, Should tables be sorted? J. Assoc. Comp. Mach. 28 (1981), 615-628.
36. A. C. Yao and F. F. Yao, A general approach to d-dimension geometric queries, in "Proc. of 17th STOC," pp. 163-168, 1985.