Given an edge weighted graph and a forest F, the 2-edge connectivity augmentation problem is to pick a minimum weighted set of edges, E', such that every connected component of E' ∪ F is 2-edge connected. Williamson et al. gave a 2-approximation algorithm (WGMV) for this problem using the primal-dual schema. We show that when edge weights are integral, the WGMV procedure can be modified to obtain a half-integral dual. The 2-edge connectivity augmentation problem has an interesting connection to routing flow in graphs where the union of supply and demand is planar. The half-integrality of the dual leads to a tight 2-approximate max-half-integral-flow min-multicut theorem.
@InProceedings{garg_et_al:LIPIcs.ESA.2020.55, author = {Garg, Naveen and Kumar, Nikhil}, title = {{Dual Half-Integrality for Uncrossable Cut Cover and Its Application to Maximum Half-Integral Flow}}, booktitle = {28th Annual European Symposium on Algorithms (ESA 2020)}, pages = {55:1--55:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-162-7}, ISSN = {1868-8969}, year = {2020}, volume = {173}, editor = {Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.55}, URN = {urn:nbn:de:0030-drops-129214}, doi = {10.4230/LIPIcs.ESA.2020.55}, annote = {Keywords: Combinatorial Optimization, Multicommodity Flow, Network Design} }
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