Sparse geometric graphs with small dilation
Computational Geometry
2009-12-07 v2
Abstract
Given a set S of n points in R^D, and an integer k such that 0 <= k < n, we show that a geometric graph with vertex set S, at most n - 1 + k edges, maximum degree five, and dilation O(n / (k+1)) can be computed in time O(n log n). For any k, we also construct planar n-point sets for which any geometric graph with n-1+k edges has dilation Omega(n/(k+1)); a slightly weaker statement holds if the points of S are required to be in convex position.
Cite
@article{arxiv.cs/0702080,
title = {Sparse geometric graphs with small dilation},
author = {Boris Aronov and Mark de Berg and Otfried Cheong and Joachim Gudmundsson and Herman Haverkort and Michiel Smid and Antoine Vigneron},
journal= {arXiv preprint arXiv:cs/0702080},
year = {2009}
}