English

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 O(nlogn)O(n\log 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.

Keywords

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}
}
R2 v1 2026-06-23T03:54:34.279Z