  We study a wireless ad-hoc sensor network (WASN) where $N$ sensors gather
data from the surrounding environment and transmit their sensed information to
$M$ fusion centers (FCs) via multi-hop wireless communications. This node
deployment problem is formulated as an optimization problem to make a trade-off
between the sensing uncertainty and energy consumption of the network. Our
primary goal is to find an optimal deployment of sensors and FCs to minimize a
Lagrange combination of the sensing uncertainty and energy consumption. To
support arbitrary routing protocols in WASNs, the routing-dependent necessary
conditions for the optimal deployment are explored. Based on these necessary
conditions, we propose a routing-aware Lloyd algorithm to optimize node
deployment. Simulation results show that, on average, the proposed algorithm
outperforms the existing deployment algorithms.
