path comprising $N$ relay nodes along a line.[]{data-label="fig:general_line_network"}](general-line-network.pdf){height="1.2cm" width="8cm"}

Our work in this paper is motivated by recent interest in problems of [*impromptu (as-you-go)*]{} deployment of wireless relay networks in various situations; for example, “first responders” in emergency situations, or quick deployment (and redeployment) of sensor networks in large terrains, such as forests (see [@souryal-etal07real-time-deployment-range-extension], [@howard-etal02incremental-self-deployment-algorithm-mobile-sensor-network], [@bao-lee07rapid-deployment-ad-hoc-backbone], [@sinha-etal12optimal-sequential-relay-placement-random-lattice-path], [@chattopadhyay-etal13measurement-based-impromptu-placement_wiopt]). In this paper, we are concerned with the situation in which a deployment agent walks [*from the source node to the sink node*]{}, along the line joining these two nodes, and places wireless relays (in an “as-you-go” manner) so as to create a source-to-sink multi-relay channel network with high data rate; see Figure \[fig:general\_line\_network\]. We first consider the scenario where the length $L$ of the line in Figure \[fig:general\_line\_network\] is known; the results of this case are used to formulate the as-you-go deployment in the case where $L$ is a priori unknown, but has exponential distribution with known mean $\overline{L}$.

In order to capture the fundamental trade-offs involved in such problems, we consider an information theoretic model. For a placement of the relay nodes and allocation of transmission powers to these relays, we model the “quality” of communication between the source 