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Dual Half-Integrality for Uncrossable Cut Cover and Its Application to Maximum Half-Integral Flow
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28th Annual European Symposium on Algorithms (ESA 2020)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: European Symposium on Algorithms (ESA) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2020-08-26
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Naveen Garg and Nikhil Kumar. Dual Half-Integrality for Uncrossable Cut Cover and Its Application to Maximum Half-Integral Flow. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 55:1-55:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.ESA.2020.55
https://doi.org/10.4230/LIPIcs.ESA.2020.55
Abstract
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.
Subject Classification
ACM Subject Classification
- Theory of computation → Routing and network design problems
Keywords
- Combinatorial Optimization
- Multicommodity Flow
- Network Design
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References
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