We study the problem of finding a minimum energy broadcast tree in duty cycled wireless sensor networks. In such networks, every node has a wakeup schedule and is awake and ready to receive packets or transmit in certain time slots during the schedule and asleep during the rest of the schedule. We assume that a forwarding node needs to stay awake to forward a packet to the next hop neighbor until the neighbor is awake. The minimum energy broadcast tree minimizes the number of additional time units that nodes have to stay awake in order to accomplish broadcast. We show that finding the minimum energy broadcast tree is NP-hard. We give two algorithms for finding energy-efficient broadcast trees in such networks. We performed extensive simulations to study the performance of these algorithms and compare them with previously proposed algorithms. Our results show that our algorithms exhibit the best performance in terms of average number of additional time units a node needs to be awake, as well as in terms of the smallest number of highly loaded nodes, while being competitive with previous algorithms in terms of the total number of transmissions and delay
