the delivery phase, each user randomly connects to $\rho$ servers. We now have a degree of freedom thanks to the additional storage space available at each server. Each user can obtain a segment from any $\rho -z$ of the $\rho$ servers it is connected to by receiving one coded subsegment from each of them. The choice of the servers that deliver the coded subsegments to the users is made such that the multicasting opportunities across the network are maximized. We construct an incidence matrix $A$ of dimensions $P \times K$ such that $a_{ij}=1$ if $S_i$ is connected to $U_j$, $a_{ij}=0$ otherwise. Consider the $(t+1)-$element subset $\mathcal{H}_i$, and the file segments $W_{d_k,\mathcal{H}_i\backslash \{ k\}}, \forall k\in \mathcal{H}_i$. Consider the columns of $A$ corresponding to the users in $\mathcal{H}_i$ and the matrix $Q$ formed by them. Define the minimum cover of $\mathcal{H}_i$ as the smallest $l$ for which a $l\times (t+1)$ submatrix of $Q$ has at least $\rho-z$ non-zero values in each column. The servers corresponding to the $l$ rows of this submatrix have to transmit one coded message each to satisfy the requests for the missing segments corresponding to $\mathcal{H}_i$. Therefore, the total number of transmissions required to deliver the segments 