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# Dual Half-Integrality for Uncrossable Cut Cover and Its Application to Maximum Half-Integral Flow

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LIPIcs.ESA.2020.55.pdf
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## Cite As

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

## 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

1. Ajit Agrawal, Philip N. Klein, and R. Ravi. When trees collide: An approximation algorithm for the generalized steiner problem on networks. SIAM J. Comput., 24(3):440-456, 1995. URL: https://doi.org/10.1137/S0097539792236237.
2. Naveen Garg, Nikhil Kumar, and András Sebő. Integer plane multiflow maximisation: Flow-cut gap and one-quarter-approximation. In International Conference on Integer Programming and Combinatorial Optimization, pages 144-157. Springer, 2020.
3. Naveen Garg, Vijay V Vazirani, and Mihalis Yannakakis. Approximate max-flow min-(multi) cut theorems and their applications. SIAM Journal on Computing, 25(2):235-251, 1996.
4. Naveen Garg, Vijay V. Vazirani, and Mihalis Yannakakis. Primal-dual approximation algorithms for integral flow and multicut in trees. Algorithmica, 18(1):3-20, 1997.
5. Michel X. Goemans and David P. Williamson. A general approximation technique for constrained forest problems. SIAM J. Comput., 24(2):296-317, 1995. URL: https://doi.org/10.1137/S0097539793242618.
6. Kamal Jain. A factor 2 approximation algorithm for the generalized steiner network problem. Combinatorica, 21(1):39-60, 2001. URL: https://doi.org/10.1007/s004930170004.
7. Philip Klein, Serge A Plotkin, and Satish Rao. Excluded minors, network decomposition, and multicommodity flow. In Proceedings of the twenty-fifth annual ACM symposium on Theory of computing, pages 682-690. ACM, 1993.
8. David P. Williamson, Michel X. Goemans, Milena Mihail, and Vijay V. Vazirani. A primal-dual approximation algorithm for generalized steiner network problems. Combinatorica, 15(3):435-454, 1995. URL: https://doi.org/10.1007/BF01299747.
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