# Well-balanced orientation

An orientation $D=(V,A)$ of a graph $G=(V,E)$ is well-balanced if
$\lambda_D(u,v) \geq \left\lfloor \frac{\lambda_G(u,v)}{2}\right\rfloor$ for every $u,v \in V$
(where $\lambda$ is the local edge-connectivity). By Nash-Williams' strong orientation theorem, every graph has a well-balanced orientation, and it can be found in polynomial time. We can also satisfy the additional property that $\lfloor d_G(v) /2 \rfloor \leq \varrho_D(v) \leq \lceil d_G(v)/2 \rceil$; an orientation with this property is called smooth.