Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
An O(n log n) algorithm for the all-nearest-neighbors problem
Discrete & Computational Geometry
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Algorithms for proximity problems in higher dimensions
Computational Geometry: Theory and Applications
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)
Finding nearest neighbors in growth-restricted metrics
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Navigating nets: simple algorithms for proximity search
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
A compact space decomposition for effective metric indexing
Pattern Recognition Letters
A Data Structure and an Algorithm for the Nearest Point Problem
IEEE Transactions on Software Engineering
Fast algorithms for the all nearest neighbors problem
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Optimal parallel all-nearest-neighbors using the well-separated pair decomposition
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
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
CM-tree: A dynamic clustered index for similarity search in metric databases
Data & Knowledge Engineering
Parallel query processing on distributed clustering indexes
Journal of Discrete Algorithms
Solving similarity joins and range queries in metric spaces with the list of twin clusters
Journal of Discrete Algorithms
Fast Approximate kNN Graph Construction for High Dimensional Data via Recursive Lanczos Bisection
The Journal of Machine Learning Research
Efficient k-nearest neighbor graph construction for generic similarity measures
Proceedings of the 20th international conference on World wide web
Novel KNN-motivation-PSO and its application to image segmentation
Proceedings of the CUBE International Information Technology Conference
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Let $\mathbb{U}$ be a set of elements and d a distance function defined among them. Let NNk(u) be the k elements in $\mathbb{U}-\{u\}$ having the smallest distance to u. The k-nearest neighbor graph (knng) is a weighted directed graph $G(\mathbb{U},E)$ such that E={(u,v), v∈NNk(u)}. Several knng construction algorithms are known, but they are not suitable to general metric spaces. We present a general methodology to construct knngs that exploits several features of metric spaces. Experiments suggest that it yields costs of the form c1n1.27 distance computations for low and medium dimensional spaces, and c2n1.90 for high dimensional ones.