Computational geometry: a retrospective
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Proceedings of the eleventh annual symposium on Computational geometry
A fast branch & bound nearest neighbour classifier in metric spaces
Pattern Recognition Letters
An optimal algorithm for approximate nearest neighbor searching
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Fixed Queries Array: A Fast and Economical Data Structure for Proximity Searching
Multimedia Tools and Applications
R-trees: a dynamic index structure for spatial searching
SIGMOD '84 Proceedings of the 1984 ACM SIGMOD international conference on Management of data
Proximity Matching Using Fixed-Queries Trees
CPM '94 Proceedings of the 5th Annual Symposium on Combinatorial Pattern Matching
Spaghettis: An Array Based Algorithm for Similarity Queries in Metric Spaces
SPIRE '99 Proceedings of the String Processing and Information Retrieval Symposium & International Workshop on Groupware
Probabilistic proximity searching algorithms based on compact partitions
Journal of Discrete Algorithms - SPIRE 2002
Engineering efficient metric indexes
Pattern Recognition Letters
t-Spanners for metric space searching
Data & Knowledge Engineering
Efficient Processing of Nearest Neighbor Queries in Parallel Multimedia Databases
DEXA '08 Proceedings of the 19th international conference on Database and Expert Systems Applications
Approximate similarity search: A multi-faceted problem
Journal of Discrete Algorithms
Speeding up spatial approximation search in metric spaces
Journal of Experimental Algorithmics (JEA)
Indexing inexact proximity search with distance regression in pivot space
Proceedings of the Third International Conference on SImilarity Search and APplications
Indexing methods for approximate dictionary searching: Comparative analysis
Journal of Experimental Algorithmics (JEA)
Scalable pattern search analysis
MCPR'11 Proceedings of the Third Mexican conference on Pattern recognition
On the least cost for proximity searching in metric spaces
WEA'06 Proceedings of the 5th international conference on Experimental Algorithms
Proximity searching in high dimensional spaces with a proximity preserving order
MICAI'05 Proceedings of the 4th Mexican international conference on Advances in Artificial Intelligence
A data allocation method for efficient content-based retrieval in parallel multimedia databases
ISPA'07 Proceedings of the 2007 international conference on Frontiers of High Performance Computing and Networking
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Proximity searches become very difficult on "high dimensional" metric spaces, that is, those whose histogram of distances has a large mean and/or a small variance. This so-called "curse of dimensionality", well known in vector spaces, is also observed in metric spaces. The search complexity grows sharply with the dimension and with the search radius. We present a general probabilistic framework applicable to any search algorithm and whose net effect is to reduce the search radius. The higher the dimension, the more effective the technique. We illustrate empirically its practical performance on a particular class of algorithms, where large improvements in the search time are obtained at the cost of a very small error probability.