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.
@InProceedings{gudmundsson_et_al:LIPIcs.ISAAC.2021.45, author = {Gudmundsson, Joachim and Sha, Yuan and Yao, Fan}, title = {{Augmenting Graphs to Minimize the Radius}}, booktitle = {32nd International Symposium on Algorithms and Computation (ISAAC 2021)}, pages = {45:1--45:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-214-3}, ISSN = {1868-8969}, year = {2021}, volume = {212}, editor = {Ahn, Hee-Kap and Sadakane, Kunihiko}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.45}, URN = {urn:nbn:de:0030-drops-154785}, doi = {10.4230/LIPIcs.ISAAC.2021.45}, annote = {Keywords: graph augmentation, radius, approximation algorithm} }
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