Computational geometry: a retrospective
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
An optimal algorithm for approximate nearest neighbor searching
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
ACM Computing Surveys (CSUR)
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
The X-tree: An Index Structure for High-Dimensional Data
VLDB '96 Proceedings of the 22th International Conference on Very Large Data Bases
Multidimensional Binary Search Trees in Database Applications
IEEE Transactions on Software Engineering
t-Spanners as a Data Structure for Metric Space Searching
SPIRE 2002 Proceedings of the 9th International Symposium on String Processing and Information Retrieval
Probabilistic Proximity Searching Algorithms Based on Compact Partitions
SPIRE 2002 Proceedings of the 9th International Symposium on String Processing and Information Retrieval
Dynamic spatial approximation trees
Journal of Experimental Algorithmics (JEA)
NM-Tree: Flexible Approximate Similarity Search in Metric and Non-metric Spaces
DEXA '08 Proceedings of the 19th international conference on Database and Expert Systems Applications
Where are you heading, metric access methods?: a provocative survey
Proceedings of the Third International Conference on SImilarity Search and APplications
Indexing inexact proximity search with distance regression in pivot space
Proceedings of the Third International Conference on SImilarity Search and APplications
Improving the similarity search of tandem mass spectra using metric access methods
Proceedings of the Third International Conference on SImilarity Search and APplications
Estimating the indexability of multimedia descriptors for similarity searching
RIAO '10 Adaptivity, Personalization and Fusion of Heterogeneous Information
On nonmetric similarity search problems in complex domains
ACM Computing Surveys (CSUR)
On fast non-metric similarity search by metric access methods
EDBT'06 Proceedings of the 10th international conference on Advances in Database Technology
Modified LSI model for efficient search by metric access methods
ECIR'05 Proceedings of the 27th European conference on Advances in Information Retrieval Research
Non-metric similarity search of tandem mass spectra including posttranslational modifications
Journal of Discrete Algorithms
Static-to-Dynamic transformation for metric indexing structures
SISAP'12 Proceedings of the 5th international conference on Similarity Search and Applications
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Range searches in metric spaces can be very difficult if the space is "high dimensional", i.e. when the 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. There are at least two reasons behind the curse of dimensionality: a large search radius and/or a high intrinsic dimension of the metric space. We present a general probabilistic framework based on stretching the triangle inequality, whose direct effect is a reduction of the effective search radius. The technique gets more effective as the dimension grows, and the basic principle can be applied to any search algorithm. In this paper we apply it to a particular class of indexing algorithms. We present an analysis which helps understand the process, as well as empirical evidence showing dramatic improvements in the search time at the cost of a very small error probability.