  Given an edge weighted graph and a forest $F$, the $\textit{2-edge
connectivity augmentation problem}$ is to pick a minimum weighted set of edges,
$E'$, such that every connected component of $E'\cup F$ 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.
