Abstract: This paper addresses the target coverage problem in wireless sensor networks. Communication and sensing consume energy, therefore efficient power management can extend network lifetime. In this paper we consider a large number of sensors randomly deployed to monitor a number of targets. Each target may be redundantly covered by multiple sensors. To conserve energy, we organize sensors in sets activated sucessively. In this paper we introduce the Connected Set Covers (CSC) problem that has as objective finding a maximum number of set covers such that each sensor node to be activated is connected to the base station. A sensor can participate in multiple sensor sets, but the total energy spent in all sets is constrained by the initial energy reserves. We show that the CSC problem is NPcomplete and we propose three solutions: an integer programming based solution, a greedy approach, and a distributed and localized heuristic. Simulation results that validate our approaches are als...