any gains, since it is not optimized for the realization of the topology.

Another line of related works study caching in combination networks [@comb1],[@comb3], which consider a single server serving cache-equipped users through multiple relay nodes. The server is connected to these relays through unicast links, which in turn serve a distinct subset of a fixed number of users through unicast links. A combination network with cache-enabled relay nodes is considered in [@comb3]. In our paper, we relax the symmetry of a standard combination network and the assumption of a fixed and known network topology, which would be unrealistic in many practical scenarios, to a certain degree by allowing each user to connect to a random fixed number of servers, thus breaking the symmetry from the servers’ perspective while maintaining the symmetry from the end-users’ perspective.\
***Notations***. For two integers $i<j$, we denote the set $\{i,i+1,\ldots, j \}$ by $[i:j]$, while the set $[1:j]$ is denoted by $[j]$. Sets are denoted with the calligraphic font, and $|\mathcal{A}|$ denotes the cardinality of set $\mathcal{A}$. For $\mathcal{A} =\{a_1,a_2,\ldots,a_p\}$, we define $X_{\mathcal{A}} \triangleq (X_{a_1}, \ldots, X_{a_p})$. $\mathbbm{1}_{E}$ denotes the indicator function of the event $E$, i.e., its value is $1$ when the event 