a line and along a random lattice path, respectively. The formulations in [@mondal-etal12impromptu-deployment_NCC] and [@sinha-etal12optimal-sequential-relay-placement-random-lattice-path] are based on the so-called “lone packet traffic model" under which, at any time instant, there can be no more than one packet traversing the network, thereby eliminating contention between wireless links. This work was later extended in [@chattopadhyay-etal13measurement-based-impromptu-placement_wiopt] to the scenario where the traffic is still lone packet, but a measurement-based approach is employed to account for the spatial variation of link qualities due to shadowing.

In this paper, we consider as-you-go deployment along a line, but move away from the lone-packet traffic assumption by employing information theoretic achievable rate formulas (for full-duplex radios and decode-and-forward relaying). We assume exponential path-loss model (see [@franceschetti-etal04random-walk-model-wave-propagation] and Section \[subsection:motivation-for-exponential-path-loss\]). To the best of our knowledge, there is no prior work that considers as-you-go deployment under this physical layer model.

Our Contribution
----------------

-   [**Optimal Offline Deployment:**]{} Given the location of $N$ full-duplex relays to connect a source and a sink separated by a given distance $L$, and under the exponential path-loss model and a sum power constraint among the nodes, the optimal power split among the nodes and the achievable rate are expressed (Theorem \[theorem:multirelay\_capacity\]) in 