Definition
Given a set P of n points in a d-dimensional space ℜd and a query point q ∈ ℜd, a nearest neighbor (NN) query is to find the set of nearest points to the query point q. Formally, \(NN\left (q\right ) = \left \{p\vert p \in P,\forall o \in P,(o\neq p),\vert qp\vert <\left \vert qo\right \vert \right \}\). In most cases, ℜd refers to a d-dimensional Euclidean space.
Main Text
Nearest neighbor search is one of the oldest problems in computer science. The NN algorithm was one of the earliest algorithms used to determine a solution to the traveling salesman problem (TSP). The NN query first appeared in Geographic Information Systems around 1990 and has now already become a frequently encountered query type in this field. Recently, several NN algorithms have been proposed for NN queries based on spatial access methods (e.g., quad-trees, R-trees). For all these algorithms, depth-first search (DFS) and breadth-first search (BFS) algorithms are two most common branch-and-bound...
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Roussopoulos N, Kelley S, Vincent F (1995) Nearest neighbor queries. In: Proceedings of the ACM SIGMOD international conference on management of data, San Jose, pp 71–79
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Chen, F., Lu, CT. (2017). Nearest Neighbor Query, Definition. In: Shekhar, S., Xiong, H., Zhou, X. (eds) Encyclopedia of GIS. Springer, Cham. https://doi.org/10.1007/978-3-319-17885-1_866
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DOI: https://doi.org/10.1007/978-3-319-17885-1_866
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