Fast Algorithms for Diameter-Optimally Augmenting Paths and Trees
Computational Geometry
2016-07-20 v1
Abstract
We consider the problem of augmenting an n-vertex graph embedded in a metric space, by inserting one additional edge in order to minimize the diameter of the resulting graph. We present exact algorithms for the cases when (i) the input graph is a path, running in O(n \log^3 n) time, and (ii) the input graph is a tree, running in O(n^2 \log n) time. We also present an algorithm that computes a (1+\eps)-approximation in O(n + 1/\eps^3) time, for paths in R^d, where d is a constant.
Cite
@article{arxiv.1607.05547,
title = {Fast Algorithms for Diameter-Optimally Augmenting Paths and Trees},
author = {Ulrike Große and Joachim Gudmundsson and Christian Knauer and Michiel Smid and Fabian Stehn},
journal= {arXiv preprint arXiv:1607.05547},
year = {2016}
}