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Augmenting Graphs to Minimize the Radius

Authors Joachim Gudmundsson, Yuan Sha, Fan Yao

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Author Details

Joachim Gudmundsson
  • The University of Sydney, Australia
Yuan Sha
  • The University of Sydney, Australia
Fan Yao
  • The University of Sydney, Australia

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Joachim Gudmundsson, Yuan Sha, and Fan Yao. Augmenting Graphs to Minimize the Radius. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 45:1-45:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ISAAC.2021.45

Abstract

We study the problem of augmenting a metric graph by adding k edges while minimizing the radius of the augmented graph. We give a simple 3-approximation algorithm and show that there is no polynomial-time (5/3-ε)-approximation algorithm, for any ε > 0, unless P = NP. 
We also give two exact algorithms for the special case when the input graph is a tree, one of which is generalized to handle metric graphs with bounded treewidth.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • graph augmentation
  • radius
  • approximation algorithm

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