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A critical issue in wireless sensor networks is to construct energy efficient virtual backbones for routing, broadcasting and data propagating. The minimum connected dominating set (MCDS) has been proposed as a backbone to reduce power dissipation and prolong network lifetime. However, we find that an MCDS cannot guarantee maximum network lifetime as it does not consider the battery discharging behavior. Recent study in battery technology reveals that the discharging of a battery is not linear. Batteries tend to discharge more power than needed, and reimburse the over-discharged power later if they have sufficiently long recovery time. In order to optimize network performance and construct an energy efficient virtual backbone in sensor networks, battery-awareness should be considered. In this paper we first study the mathematical battery discharging model and provide a simplified battery model suitable for implementation in sensor networks. We then introduce the concept of battery-aware connected dominating set (BACDS) and show that in general the BACDS can achieve longer lifetime than the MCDS. Then we show that finding a minimum BACDS (MBACDS) is NP-hard and give a distributed approximation algorithm to construct the BACDS. The resulting BACDS constructed by our algorithm is at most (8+Δ)opt size where Δ is the maximum node degree and opt is the size of an optimal BACDS. The time and message complexities of the algorithm are O(n) and O(n(√n+logn+Δ)), respectively, where n is the number of nodes in the network. The simulation results show that the BACDS constructed by our algorithm can save a significant amount of energy and achieve up to 30% longer network lifetime than the MCDS. To the best of our knowledge, this is the first work considering battery-awareness in the construction of connected dominating sets.