Data structures and network algorithms
Data structures and network algorithms
Computational geometry: an introduction
Computational geometry: an introduction
The ultimate planar convex hull algorithm
SIAM Journal on Computing
Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Recent trends in hierarchic document clustering: a critical review
Information Processing and Management: an International Journal
Euclidean minimum spanning trees and bichromatic closest pairs
Discrete & Computational Geometry
A survey of adaptive sorting algorithms
ACM Computing Surveys (CSUR)
Faster algorithms for some geometric graph problems in higher dimensions
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Adaptive set intersections, unions, and differences
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
A minimum spanning tree algorithm with inverse-Ackermann type complexity
Journal of the ACM (JACM)
An Algorithm for Finding Best Matches in Logarithmic Expected Time
ACM Transactions on Mathematical Software (TOMS)
An optimal minimum spanning tree algorithm
Journal of the ACM (JACM)
Finding nearest neighbors in growth-restricted metrics
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A Faster Deterministic Algorithm for Minimum Spanning Trees
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Finding Minimum Spanning Trees in O(m alpha(m,n)) Time
Finding Minimum Spanning Trees in O(m alpha(m,n)) Time
Cover trees for nearest neighbor
ICML '06 Proceedings of the 23rd international conference on Machine learning
Graph-Theoretical Methods for Detecting and Describing Gestalt Clusters
IEEE Transactions on Computers
Fast Algorithms for Constructing Minimal Spanning Trees in Coordinate Spaces
IEEE Transactions on Computers
A discriminative framework for clustering via similarity functions
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
SFCS '75 Proceedings of the 16th Annual Symposium on Foundations of Computer Science
Scalable parallel minimum spanning forest computation
Proceedings of the 17th ACM SIGPLAN symposium on Principles and Practice of Parallel Programming
Kinetic Euclidean minimum spanning tree in the plane
Journal of Discrete Algorithms
MLPACK: a scalable C++ machine learning library
The Journal of Machine Learning Research
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The Euclidean Minimum Spanning Tree problem has applications in a wide range of fields, and many efficient algorithms have been developed to solve it. We present a new, fast, general EMST algorithm, motivated by the clustering and analysis of astronomical data. Large-scale astronomical surveys, including the Sloan Digital Sky Survey, and large simulations of the early universe, such as the Millennium Simulation, can contain millions of points and fill terabytes of storage. Traditional EMST methods scale quadratically, and more advanced methods lack rigorous runtime guarantees. We present a new dual-tree algorithm for efficiently computing the EMST, use adaptive algorithm analysis to prove the tightest (and possibly optimal) runtime bound for the EMST problem to-date, and demonstrate the scalability of our method on astronomical data sets.