Randomized Incremental Construction of Net-Trees
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Net-trees are a general purpose data structure for metric data that have been used to solve a wide range of algorithmic problems. We give a simple randomized algorithm to construct net-trees on doubling metrics using O(n n) time in expectation. Along the way, we define a new, linear-size net-tree variant that simplifies the analyses and algorithms. We show a connection between these trees and approximate Voronoi diagrams and use this to simplify the point location necessary in net-tree construction. Our analysis uses a novel backwards analysis that may be of independent interest.
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