Skip lists: a probabilistic alternative to balanced trees
Communications of the ACM
K-d trees for semidynamic point sets
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Higher-dimensional Voronoi diagrams in linear expected time
Discrete & Computational Geometry
Euclidean minimum spanning trees and bichromatic closest pairs
Discrete & Computational Geometry
Surpassing the information theoretic bound with fusion trees
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
A randomized linear-time algorithm to find minimum spanning trees
Journal of the ACM (JACM)
LEDA: a platform for combinatorial and geometric computing
Communications of the ACM
Dealing with higher dimensions: the well-separated pair decomposition and its applications
Dealing with higher dimensions: the well-separated pair decomposition and its applications
The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
Faster algorithms for some geometric graph problems in higher dimensions
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Optimal Expected-Time Algorithms for Closest Point Problems
ACM Transactions on Mathematical Software (TOMS)
The Quadtree and Related Hierarchical Data Structures
ACM Computing Surveys (CSUR)
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
Minimum Spanning Trees in d Dimensions
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
A Faster Deterministic Algorithm for Minimum Spanning Trees
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Geometric minimum spanning trees with GEOFILTERKRUSKAL*
SEA'10 Proceedings of the 9th international conference on Experimental Algorithms
Output-sensitive well-separated pair decompositions for dynamic point sets
Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
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Let S be a set of n points inℜd. We present an algorithm that uses thewell-separated pair decomposition and computes the minimum spanningtree of S under any Lp or polyhedralmetric. A theoretical analysis shows that it has an expectedrunning time of O(n log n) for uniform pointdistributions; this is verified experimentally. Extensiveexperimental results show that this approach is practical. Under avariety of input distributions, the resulting implementation isrobust and performs well for points in higher dimensionalspace.