SIAM Journal on Computing
Maintenance of geometric extrema ∈
Journal of the ACM (JACM)
Euclidean minimum spanning trees and bichromatic closest pairs
Discrete & Computational Geometry
Optimal time bounds for some proximity problems in the plane
Information Processing Letters
Farthest neighbors, maximum spanning trees and related problems in higher dimensions
Computational Geometry: Theory and Applications
Maximum distance between two sets of points in Ed
Pattern Recognition Letters - Special issue on computational geometry
On the maximum degree of minimum spanning trees
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
A Hyperplane Incidence Problem with Applications to Counting Distances
SIGAL '90 Proceedings of the International Symposium on Algorithms
Minimum Spanning Trees in d Dimensions
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
Divide-and-conquer in multidimensional space
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
SFCS '75 Proceedings of the 16th Annual Symposium on Foundations of Computer Science
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Given a set of n points in some d-dimensional Euclidean space, each point colored with one of k( 驴 2) colors, a bichromatic closest (resp., farthest) pair is a closest (resp., farthest) pair of points of different colors. We present efficient algorithms to compute a bichromatic closest pair and a bichromatic farthest pair. We consider both static, and dynamic versions with respect to color flips. We also give some combinatorial bounds on the multiplicities of extreme distances in this setting.