Randomized Incremental Construction of Net-Trees
Computational Geometry
2018-09-06 v1
Abstract
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 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.
Cite
@article{arxiv.1809.01308,
title = {Randomized Incremental Construction of Net-Trees},
author = {Mahmoodreza Jahanseir and Donald R. Sheehy},
journal= {arXiv preprint arXiv:1809.01308},
year = {2018}
}