This paper addresses a graph optimization problem, called the Witness Tree problem, which seeks a spanning tree of a graph minimizing a certain non-linear objective function. This problem is of interest because it plays a crucial role in the analysis of the best approximation algorithms for two fundamental network design problems: Steiner Tree and Node-Tree Augmentation. We will show how a wiser choice of witness trees leads to an improved approximation for Node-Tree Augmentation, and for Steiner Tree in special classes of graphs.
@InProceedings{hyattdenesik_et_al:LIPIcs.ICALP.2023.79, author = {Hyatt-Denesik, Dylan and Jabal Ameli, Afrouz and Sanit\`{a}, Laura}, title = {{Finding Almost Tight Witness Trees}}, booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)}, pages = {79:1--79:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-278-5}, ISSN = {1868-8969}, year = {2023}, volume = {261}, editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.79}, URN = {urn:nbn:de:0030-drops-181314}, doi = {10.4230/LIPIcs.ICALP.2023.79}, annote = {Keywords: Algorithms, Network Design, Approximation} }
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