5.5.0.0.3 Algorithm:

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Each connected component ($VDC$, $VDC'$, $VDC''$, etc) represents one particular assignment of $vm_{i} \in VM$ to $vd_{i} \in VD$, i.e. a particular $vmap$ meeting all the $vmap$ requirements

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So from amongst all such possible connected components (assignments) we choose that which has the least cost associated with it, i.e. $\sum_{\forall vd_i,vd_j \in VDC'} cost(vde_{i,j})$ is minimum over the set of all possible connected components

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This is equivalent to enumerating all the possible connected components of size $\mid$ VM $\mid$ and then choosing the one which has the least cost associated with it.