Data structures and algorithms 3: multi-dimensional searching and computational geometry
Data structures and algorithms 3: multi-dimensional searching and computational geometry
Minimum diameter spanning trees and related problems
SIAM Journal on Computing
An optimal algorithm for intersecting three-dimensional convex polyhedra
SIAM Journal on Computing
An efficient algorithm for the Euclidean two-center problem
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Intersection of unit-balls and diameter of point set in R3
Computational Geometry: Theory and Applications
Computational geometry in C (2nd ed.)
Computational geometry in C (2nd ed.)
Faster construction of planar two-centers
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Facility Location and the Geometric Minimum-Diameter Spanning Tree
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Semi-Online Maintenance of Geometric Optima and Measures
SIAM Journal on Computing
Facility location and the geometric minimum-diameter spanning tree
Computational Geometry: Theory and Applications - Special issue on computational geometry - EWCG'02
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In this paper we consider finding a geometric minimum-sum dipolar spanning tree in R^3, and present an algorithm that takes O(n^2log^2n) time using O(n^2) space, thus almost matching the best known results for the planar case. Our solution uses an interesting result related to the complexity of the common intersection of n balls in R^3, of possible different radii, that are all tangent to a given point p. The problem has applications in communication networks, when the goal is to minimize the distance between two hubs or servers as well as the distance from any node in the network to the closer of the two hubs.