We consider the problem of finding a shortcut connecting two vertices of a graph that minimizes the diameter of the resulting graph. We present an O(n^2 log^3 n)-time algorithm using linear space for the case that the input graph is a tree consisting of n vertices. Additionally, we present an O(n^2 log^3 n)-time algorithm using linear space for a continuous version of this problem.
@InProceedings{oh_et_al:LIPIcs.ISAAC.2016.59, author = {Oh, Eunjin and Ahn, Hee-Kap}, title = {{A Near-Optimal Algorithm for Finding an Optimal Shortcut of a Tree}}, booktitle = {27th International Symposium on Algorithms and Computation (ISAAC 2016)}, pages = {59:1--59:12}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-026-2}, ISSN = {1868-8969}, year = {2016}, volume = {64}, editor = {Hong, Seok-Hee}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2016.59}, URN = {urn:nbn:de:0030-drops-68283}, doi = {10.4230/LIPIcs.ISAAC.2016.59}, annote = {Keywords: Network Augmentation, Shortcuts, Diameter, Trees} }
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