Minimum Dilation Stars
Computational Geometry
2007-06-14 v3
Abstract
The dilation of a Euclidean graph is defined as the ratio of distance in the graph divided by distance in R^d. In this paper we consider the problem of positioning the root of a star such that the dilation of the resulting star is minimal. We present a deterministic O(n log n)-time algorithm for evaluating the dilation of a given star; a randomized O(n log n) expected-time algorithm for finding an optimal center in R^d; and for the case d=2, a randomized O(n 2^(alpha(n)) log^2 n) expected-time algorithm for finding an optimal center among the input points.
Keywords
Cite
@article{arxiv.cs/0412025,
title = {Minimum Dilation Stars},
author = {David Eppstein and Kevin A. Wortman},
journal= {arXiv preprint arXiv:cs/0412025},
year = {2007}
}
Comments
6 pages, 3 figures