Optimization of wireless sensor networks deployment with coverage and connectivity constraints

Wireless sensor networks have been widely deployed in the last decades to provide various services, like environmental monitoring or object tracking. Such a network is composed of a set of sensor nodes which are used to sense and transmit collected information to a base station. To achieve this goal, two properties have to be guaranteed: (i) the sensor nodes must be placed such that all the environment of interest is covered, and (ii) every sensor node can transmit its data to the base station (through other sensor nodes). In this paper, we consider the Minimum Connected Coverage (MCC) problem. We propose two mathematical programming formulations for the MCC problem on square grid graphs. We compare them to a recent model proposed by Rebai et al [1]. Our mathematical programming formulations yield a better LP-bound at the root of the branch-and-cut process than the model of Rebai et al. Moreover, the presented formulations outperform the proportion of solved instances in their work as well as the CPU computation time and the number of nodes explored in the tree search.