An algorithm for finding nearest neighbours in (approximately) constant average time
Pattern Recognition Letters
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
A Graph-Theoretic Game and its Application to the $k$-Server Problem
SIAM Journal on Computing
On bisectors for different distance functions
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Data structures and algorithms for nearest neighbor search in general metric spaces
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
On the approximability of numerical taxonomy (fitting distances by tree metrics)
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Distinctive Image Features from Scale-Invariant Keypoints
International Journal of Computer Vision
Counting Distance Permutations
SISAP '08 Proceedings of the First International Workshop on Similarity Search and Applications (sisap 2008)
Measuring the difficulty of distance-based indexing
SPIRE'05 Proceedings of the 12th international conference on String Processing and Information Retrieval
Using the k-nearest neighbor graph for proximity searching in metric spaces
SPIRE'05 Proceedings of the 12th international conference on String Processing and Information Retrieval
Convex Distance Functions In 3-Space Are Different
Fundamenta Informaticae
CoPhIR Image Collection under the Microscope
SISAP '09 Proceedings of the 2009 Second International Workshop on Similarity Search and Applications
Ptolemaic indexing of the signature quadratic form distance
Proceedings of the Fourth International Conference on SImilarity Search and APplications
Large-scale similarity data management with distributed Metric Index
Information Processing and Management: an International Journal
Use of permutation prefixes for efficient and scalable approximate similarity search
Information Processing and Management: an International Journal
Modelling efficient novelty-based search result diversification in metric spaces
Journal of Discrete Algorithms
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Distance permutation indexes support fast proximity searching in high-dimensional metric spaces. Given some fixed reference sites, for each point in a database the index stores a permutation naming the closest site, the second-closest, and so on. We examine how many distinct permutations can occur as a function of the number of sites and the size of the space. We give theoretical results for tree metrics and vector spaces with L"1, L"2, and L"~ metrics, improving on the previous best known storage space in the vector case. We also give experimental results and commentary on the number of distance permutations that actually occur in a variety of vector, string, and document databases.