5.5.0.0.1 Input:

$\bullet$

$G_{vm}$, $G_{vmd}$, and their associated functions

$\bullet$

an existing $vmap$

$\bullet$

a connected component $VDC \subseteq VD$ such that $\forall vd_{i} \in$ $VDC$ there $\exists$ at least one $vm_{i} \in$ $VM$ such that $vmap(vm_{i}) = vd_{i}$

$\bullet$

a cost value $cost(vde_{i,j})$ $\forall vde_{i,j} \in VDE$