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

Naveen Garg, Nikhil Kumar, Peter Sanders, Grzegorz Herman, Fabrizio Grandoni
2020 European Symposium on Algorithms  
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
more » ... 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.
doi:10.4230/lipics.esa.2020.55 dblp:conf/esa/GargK20 fatcat:fukv475af5f7ln3gejcwo425pa