Fast euclidean minimum spanning tree

Abstract

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.