Algorithms for Diameters of Unicycle Graphs and Diameter-Optimally Augmenting Trees
Data Structures and Algorithms
2020-11-20 v1 Computational Geometry
Abstract
We consider the problem of computing the diameter of a unicycle graph (i.e., a graph with a unique cycle). We present an O(n) time algorithm for the problem, where n is the number of vertices of the graph. This improves the previous best O(n \log n) time solution [Oh and Ahn, ISAAC 2016]. Using this algorithm as a subroutine, we solve the problem of adding a shortcut to a tree so that the diameter of the new graph (which is a unicycle graph) is minimized; our algorithm takes O(n^2 \log n) time and O(n) space. The previous best algorithms solve the problem in O(n^2 \log^3 n) time and O(n) space [Oh and Ahn, ISAAC 2016], or in O(n^2) time and O(n^2) space [Bil\`o, ISAAC 2018].
Cite
@article{arxiv.2011.09591,
title = {Algorithms for Diameters of Unicycle Graphs and Diameter-Optimally Augmenting Trees},
author = {Haitao Wang and Yiming Zhao},
journal= {arXiv preprint arXiv:2011.09591},
year = {2020}
}
Comments
A preliminary version will appear in WALCOM 2021