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Issue No. 05 - September (1983 vol. 9)
ISSN: 0098-5589
pp: 631-634
I. Kalantari , Department of Mathematics, Western Illinois University
In this paper we present a tree structure for storing points from a normed space whose norm is effectively computable. We then give an algorithm for finding the nearest point from the tree to a given query point. Our algorithm searches the tree and uses the triangle inequality to eliminate searching of the entirety of some branches of the tree whenever a certain predicate is satisfied. Our data structure uses 0(n) for storage. Empirical data which we have gathered suggest that the expected complexity for preprocessing and the search time are, respectively, 0(nlogn) and 0(logn).
triangle inequality, Algorithm, computational time, data structure, nearest point problem, preprocessing, storage binary search, trees

I. Kalantari and G. McDonald, "A Data Structure and an Algorithm for the Nearest Point Problem," in IEEE Transactions on Software Engineering, vol. 9, no. , pp. 631-634, 1983.
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