Computational geometry: an introduction
Computational geometry: an introduction
Higher-dimensional Voronoi diagrams in linear expected time
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Euclidean minimum spanning trees and bichromatic closest pairs
Discrete & Computational Geometry
An O(log m) parallel algorithm for the minimum spanning tree problem
Information Processing Letters
A randomized linear-time algorithm for finding minimum spanning trees
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
A randomized linear-time algorithm to find minimum spanning trees
Journal of the ACM (JACM)
Dealing with higher dimensions: the well-separated pair decomposition and its applications
Dealing with higher dimensions: the well-separated pair decomposition and its applications
ACM Computing Surveys (CSUR)
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
An optimal algorithm for approximate nearest neighbor searching fixed dimensions
Journal of the ACM (JACM)
Optimal Expected-Time Algorithms for Closest Point Problems
ACM Transactions on Mathematical Software (TOMS)
Introduction to Algorithms
OpenMP: An Industry-Standard API for Shared-Memory Programming
IEEE Computational Science & Engineering
Minimum spanning trees in d dimensions
Nordic Journal of Computing
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
Scaling and related techniques for geometry problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Lower bounds for fundamental geometric problems
Lower bounds for fundamental geometric problems
Geometric Minimum Spanning Trees via Well-Separated Pair Decompositions
Journal of Experimental Algorithmics (JEA)
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Geometric Data Structures for Computer Graphics
Geometric Data Structures for Computer Graphics
MCSTL: the multi-core standard template library
Proceedings of the 12th ACM SIGPLAN symposium on Principles and practice of parallel programming
Graph-Theoretical Methods for Detecting and Describing Gestalt Clusters
IEEE Transactions on Computers
Well-separated pair decomposition in linear time?
Information Processing Letters
Radix sorting with no extra space
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Parallel construction of k-nearest neighbor graphs for point clouds
SPBG'08 Proceedings of the Fifth Eurographics / IEEE VGTC conference on Point-Based Graphics
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Let P be a set of points in ℝd. We propose GeoFilterKruskal, an algorithm that computes the minimum spanning tree of P using well separated pair decomposition in combination with a simple modification of Kruskal’s algorithm. When P is sampled from uniform random distribution, we show that our algorithm takes one parallel sort plus a linear number of additional steps, with high probability, to compute the minimum spanning tree. Experiments show that our algorithm works better in practice for most data distributions compared to the current state of the art [31]. Our algorithm is easy to parallelize and to our knowledge, is currently the best practical algorithm on multi-core machines for d2.