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

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WALCOM: Algorithms and Computation (WALCOM 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12635))

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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 [Bilò, ISAAC 2018].

This research was supported in part by NSF under Grant CCF-2005323.

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Authors and Affiliations

  1. Department of Computer Science, Utah State University, Logan, UT, 84322, USA

    Haitao Wang & Yiming Zhao

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  1. Haitao Wang
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  2. Yiming Zhao
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Correspondence to Yiming Zhao .

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Editors and Affiliations

  1. Japan Advanced Institute of Science and Technology, Ishikawa, Japan

    Ryuhei Uehara

  2. University of Sydney, Sydney, NSW, Australia

    Seok-Hee Hong

  3. Indian Statistical Institute, kolkata, India

    Subhas C. Nandy

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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

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  • DOI: https://doi.org/10.1007/978-3-030-68211-8_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-68210-1

  • Online ISBN: 978-3-030-68211-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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