Optimal point location in a monotone subdivision
SIAM Journal on Computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Finding the upper envelope of n line segments in O(n log n) time
Information Processing Letters
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Constructing Levels in Arrangements and Higher Order Voronoi Diagrams
SIAM Journal on Computing
Efficiently computing the closest point to a query line
Pattern Recognition Letters
The widest k-dense corridor problems
Information Processing Letters
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Simplex Range Searching and k Nearest Neighbors of a Line Segment in 2D
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
A comprehensive system for locating medical services
Proceedings of the 6th International Conference on PErvasive Technologies Related to Assistive Environments
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In this paper, we present an algorithm for finding k nearest neighbors of a given query line among a set of points distributed arbitrarily on a two dimensional plane. Our algorithm requires O(n2) time and space to preprocess the given set of points, and it answers the query for a given line in O(k+logn) time, where k may also be an input at the query time. Almost a similar technique is applicable for finding the k farthest neighbors of a query line, keeping the time and space complexities invariant. We also discuss some constrained version of the problems where the preprocessing time and space complexities can be reduced keeping the query times unchanged.