node placement and the transmission schedule. Reference [@firouzabadi-martins08optimal-node-placement] is one such work where the authors considered placing a set of nodes in an existing network such that a certain network utility is optimized subject to a set of linear constraints on link rates, under the link scheduling and interference model. They posed the problem as one of geometric programming assuming exponential path-loss, and proposed a distributed solution. The authors of [@zheng-etal12robust-relay-placement_arxiv] consider relay placement for utility maximization, assuming there are several source nodes, sink nodes and a few candidate locations for placing relays; they ignore interference because of highly directional antennas used in $60$ GHz mmWave networks, which may not always be valid. Relay placement for capacity enhancement has been studied in [@lu-etal11relay-placement-80216], but there interference is mitigated by scheduling transmissions over multiple channels.

On the other hand, an information theoretic model for a wireless network often provides a closed-form expression for the channel capacity, or at least an achievable rate region. These results are asymptotic, and make idealized assumptions such as full-duplex radios, perfect interference cancellation, etc., but provide algebraic expressions that can be used to formulate tractable optimization problems which can provide useful insights. In the context of 