Computational geometry: an introduction
Computational geometry: an introduction
Minimum spanning trees in k-dimensional space
SIAM Journal on Computing
Euclidean minimum spanning trees and bichromatic closest pairs
Discrete & Computational Geometry
Faster algorithms for some geometric graph problems in higher dimensions
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Optimal Algorithms for Complete Linkage Clustering in d Dimensions
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Abstract Voronoi Diagrams and their Applications
CG '88 Proceedings of the International Workshop on Computational Geometry on Computational Geometry and its Applications
Scaling and related techniques for geometry problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Fast expected-time and approximation algorithms for geometric minimum spanning trees
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Approximate Distance Oracles Revisited
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Approximating the minimum weight spanning tree of a set of points in the Hausdorff metric
Computational Geometry: Theory and Applications
Geometric minimum spanning trees with GEOFILTERKRUSKAL*
SEA'10 Proceedings of the 9th international conference on Experimental Algorithms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Spanners for geometric intersection graphs
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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It is shown that a minimum spanning tree of n points in Rd under any fixed Lp-metric, with p = 1, 2,..., ∞, can be computed in optimal O(Td(n, n)) time in the algebraic computational tree model. Td(n, m) denotes the time to find a bichromatic closest pair between n red points and m blue points. The previous bound in the model was O(Td(n, n)log n) and it was proved only for the L2 (Euclidean) metric. Furthermore, for d = 3 it is shown that a minimum spanning tree can be found in O(n log n) time under the L1 and L∞-metrics. This is optimal in the algebraic computation tree model. The previous bound was O(n log n log log n).