and the sink by the information theoretic achievable rate of the multi-relay channel (see [@cover-gamal79capacity-relay-channel], [@reznik-etal04degraded-gaussian-multirelay-channel] and [@xie-kumar04network-information-theory-scaling-law] for the single and multi-relay channel models). The relays are equipped with full-duplex radios[^4], and carry out decode-and-forward relaying. We consider scalar, memoryless, time-invariant, additive white Gaussian noise (AWGN) channels. We assume synchronous operation across all transmitters and receivers, and consider the exponential path-loss model for radio wave propagation.

Related Work {#subsection:related_work}
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A formulation of the relay placement problem requires a model of the wireless network at the physical (PHY) and medium access control (MAC) layers. Most researchers have adopted the link scheduling and interference model, i.e., a scheduling algorithm determines radio resource allocation (channel and power) and interference is treated as noise (see [@georgiadis-etal06resource-allocation-cross-layer-control]); treating interference as noise leads to the model that simultaneous transmissions “collide” at receiving nodes, and transmission scheduling aims to avoid collisions.

However, node placement for throughput maximization with this model is intractable because the optimal throughput is obtained by first solving for the optimum schedule assuming fixed node locations, followed by an optimization over those locations. Hence, with such a model, there appears to be little work on the problem of jointly optimizing the relay 