Hardness of nearest neighbor under L-infinity

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

Volumn , Issue , 2008, Pages 424-433

  Andoni, Alexandr ^a   Croitoru, Dorian ^a   Pǎtraşcu, Mihai ^a  

^a MIT MEDIA LAB   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMMUNICATION COMPLEXITIES; LOWER BOUNDS; NEAREST NEIGHBOR SEARCHES; NEAREST NEIGHBORS;

COMPUTERS; CONTROL THEORY; DECISION THEORY; DECISION TREES; FIBER OPTIC CHEMICAL SENSORS; FILE ORGANIZATION; MATHEMATICAL MODELS; TREES (MATHEMATICS);

DATA STRUCTURES;

EID: 57949114586     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FOCS.2008.89     Document Type: Conference Paper

References (19)

1. ∞ nearest neighbor search in high dimensions. In Proc. ACM Symposium on Computational Geometry, pages 157-163, 2001.
2. 1 non-embeddability barrier: Algorithms for product metrics. Manuscript, 2008.
3. Ronald Fagin. Combining fuzzy information from multiple systems. In Proc. ACM Symposium on Principles of Database Systems, pages 216-227, 1996.
4. Ronald Fagin. Fuzzy queries in multimedia database systems (invited paper). In Proc. ACM Symposium on Principles of Database Systems, 1998.
5. Martin Farach-Colton and Piotr Indyk. Approximate nearest neighbor algorithms for hausdorff metrics via embeddings. In Proc. IEEE Symposium on Foundations of Computer Science, 1999.
6. Piotr Indyk. Approximate algorithms for high-dimensional geometric problems. Invited talk at DIMACS Workshop on Computational. Geometry'02. http://people.csail.mit.edu/indyk/high.ps, 2001.
7. ∞ norm. Journal of Computer and System Sciences, 63(4), 2001. See also FOCS'98.
8. Piotr Indyk. Approximate nearest neighbor algorithms for Frechet metric via product metrics. In Proc. ACM Symposium on Computational Geometry, 2002.
9. T. S. Jayram, Subhash Khot, Ravi Kumar, and Yuval Rabani. Cell-probe lower bounds for the partial match problem. Journal of Computer and Systems Sciences, 69(3):435-447, 2004. See also STOC'03.
10. R. Krauthgamer, J. R. Lee, M. Mendel, and A. Naor. Measured descent: A new embedding method for finite metrics. Geom. Funct Anal., 15(4):839-858, 2005.
11. Eyal Kushilevitz and Noam Nisan. Communication Complexity. Cambridge University Press, 1997.
12. I. Kremer, N. Nisan, and D. Ron. On randomized one-round communication complexity. Computational Complexity, 8(1):21-49, 1999.
13. N. Linial, E. London, and Y. Rabinovich. The geometry of graphs and some of its algorithmic applications. In Proc. IEEE Symposium on Foundations of Computer Science, pages 577-591, 1994.
14. J. Matoušek. On the distortion required for embedding finite metric spaces into normed spaces. Israel Journal of Mathematics, 93:333-344, 1996.
15. P. B. Miltersen, N. Nisan, S. Safra, and A. Wigderson. Data structures and asymmetric communication complexity. Journal of Computer and System Sciences, 1998.
16. Mihai Pǎtraşcu. (Data) STRUCTURES. In Proc. IEEE Symposium on Foundations of Computer Science, 2008.
17. Satish Rao. Small distortion and volume preserving embeddings for planar and Euclidean metrics. In Proc. ACMSymposium on Computational Geometry, pages 300-306, New York, 1999. ACM.
18. H. Samet. Foundations of Multidimensional and Metric Data Structures. Elsevier, 2006.
19. G. Shakhnarovich, T. Darrell, and P. Indyk, editors. Nearest Neighbor Methods in Learning and Vision. Neural Processing Information Series, MIT Press, 2006.