Optimal point location in a monotone subdivision
SIAM Journal on Computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Lower bounds for orthogonal range searching: part II. The arithmetic model
Journal of the ACM (JACM)
Finding the upper envelope of n line segments in O(n log n) time
Information Processing Letters
Introduction to algorithms
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
The discrepancy method: randomness and complexity
The discrepancy method: randomness and complexity
Computational Geometry: Theory and Applications
A comprehensive system for locating medical services
Proceedings of the 6th International Conference on PErvasive Technologies Related to Assistive Environments
| Hi-index | 5.23 |
We present an algorithm for finding k nearest neighbors of a given query line among a set of n points distributed arbitrarily on a two-dimensional plane. Our algorithm requires O(n2) time and O(n2/log n) space to preprocess the given set of points, and it answers the query for a given line in O(k + log n) time, where k may also be an input at the query time. Almost a similar technique works for finding k farthest neighbors of a query line, keeping the time and space complexities invariant. We also show that if k is known at the time of preprocessing, the time and space complexities for the preprocessing can be reduced keeping the query times unchanged.