Deployment of sensors in a network-like environment

This paper considers a deployment problem involving omnidirectional sensors with potentially limited sensing radius. The environment is modeled as a network and two optimization problems are formulated and solved. The first one introduces some simplifications, allowing sensors to be located everywhere in the polytope enclosing the network, and considering a reduced model for the environment called collapsed network. It is made up of a finite discrete set of points, barycenters, produced by collapsing the network edges. The second problem considers a classical graph model and forces sensors to stay on the network. We propose a discrete-time gradient ascent algorithm to find a local optimum for these problems. The present algorithm can also be implemented in a distributed fashion.