Computational geometry: an introduction
Computational geometry: an introduction
A linear time algorithm for finding all farthest neighbors in a convex polygon
Information Processing Letters
An O(n log n) algorithm for the all-nearest-neighbors problem
Discrete & Computational Geometry
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Farthest neighbors, maximum spanning trees and related problems in higher dimensions
Computational Geometry: Theory and Applications
Construction of 1-d lower envelopes and applications
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
An efficient algorithm for the three-dimensional diameter problem
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
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Let N be a set of n points in convex position in R3. The farthest-point Voronoi diagram of N partitions R3 into n convex cells. We consider the intersection G(N) of the diagram with the boundary of the convex hull of N. We give an algorithm that computes an implicit representation of G(N) in expected O(n log2 n) time. More precisely, we compute the combinatorial structure of G(N), the coordinates of its vertices, and the equation of the plane defining each edge of G(N). The algorithm allows us to solve the all-pairs farthest neighbor problem for N in expected time O(n log2n), and to perform farthest-neighbor queries on N in O(log2n) time with high probability. This can be applied to find a Euclidean maximum spanning tree and a diameter 2-clustering of N in expected O(n log4 n) time.