Algorithms for Diameters of Unicycle Graphs and Diameter-Optimally Augmenting Trees
Author ORCID Identifier
Haitao Wang https://orcid.org/0000-0001-8134-7409
International Workshop on Algorithms and Computation 2021
NSF, Division of Computing and Communication Foundations (CCF) 2005323
NSF, Division of Computing and Communication Foundations (CCF)
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(n2 log n) time and O(n) space. The previous best algorithms solve the problem in O(n2 log3 n) time and O(n) space [Oh and Ahn, ISAAC 2016], or in O(n2) time and O(n2) space [Bilò, ISAAC 2018].
Wang H., Zhao Y. (2021) Algorithms for Diameters of Unicycle Graphs and Diameter-Optimally Augmenting Trees. In: Uehara R., Hong SH., Nandy S.C. (eds) WALCOM: Algorithms and Computation. WALCOM 2021. Lecture Notes in Computer Science, vol 12635. Springer, Cham. https://doi.org/10.1007/978-3-030-68211-8_3