The Curse of Medium Dimension for Geometric Problems in Almost Every Norm

arXiv: Computational Geometry, Volume abs/1608.03245, 2016.

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Abstract:

Given a point-set, finding the Closest Pair of points in the set, determining its Diameter, and computing a Euclidean Minimum Spanning Tree are amongst the most fundamental problems in Computer Science and Computational Geometry. In this paper, we study the complexity of these three problems in medium dimension, i.e., dimension $d=Theta(l...More

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