Computational geometry: an introduction
Computational geometry: an introduction
Information and Control
Optimal point location in a monotone subdivision
SIAM Journal on Computing
A linear time algorithm for finding all farthest neighbors in a convex polygon
Information Processing Letters
A linear-time algorithm for computing the Voronoi diagram of a convex polygon
Discrete & Computational Geometry
An O(n log n) algorithm for the all-nearest-neighbors problem
Discrete & Computational Geometry
Introduction to algorithms
Farthest neighbors, maximum spanning trees and related problems in higher dimensions
Computational Geometry: Theory and Applications
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Efficiently computing the closest point to a query line
Pattern Recognition Letters
Queries with segments in Voronoi diagrams
Computational Geometry: Theory and Applications
Polygonal path approximation with angle constraints
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
ACM SIGACT News
Facility Location and the Geometric Minimum-Diameter Spanning Tree
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Computing farthest neighbors on a convex polytope
Theoretical Computer Science - Computing and combinatorics
Using simplicial partitions to determine a closest point to a query line
Pattern Recognition Letters
Facility location and the geometric minimum-diameter spanning tree
Computational Geometry: Theory and Applications - Special issue on computational geometry - EWCG'02
Polygonal chain approximation: a query based approach
Computational Geometry: Theory and Applications
Optimal simplification of polygonal chains for subpixel-accurate rendering
Computational Geometry: Theory and Applications
Computational Geometry: Theory and Applications
Constrained minimum enclosing circle with center on a query line segment
Computational Geometry: Theory and Applications
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In this paper we discuss farthest-point problems in which a set or sequence S of n points in the plane is given in advance and can be preprocessed to answer various queries efficiently. First, we give a data structure that can be used to compute the point farthest from a query line segment in O(log2 n) time. Our data structure needs O(n log n) space and preprocessing time. To the best of our knowledge no solution to this problem has been suggested yet. Second, we show how to use this data structure to obtain an output-sensitive query-based algorithm for polygonal path simplification. Both results are based on a series of data structures for fundamental farthest-point queries that can be reduced to each other.