Algorithms for Diameters of Unicycle Graphs and Diameter-Optimally Augmenting Trees

Document Type

Conference Paper

Author ORCID Identifier

Haitao Wang https://orcid.org/0000-0001-8134-7409

Journal/Book Title/Conference

International Workshop on Algorithms and Computation 2021



Publication Date


Award Number

NSF, Division of Computing and Communication Foundations (CCF) 2005323


NSF, Division of Computing and Communication Foundations (CCF)

First Page


Last Page



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].