On the complexity and distributed construction of energy-efficient broadcast trees in wireless ad hoc networks

This paper addresses the energy-efficient broadcasting problem in ad hoc wireless networks. First, we show that finding the minimum-energy broadcast tree is NP-complete. We then develop a distributed clustering algorithm that computes energy-efficient broadcast trees in polynomial time. Our distributed algorithm computes all N possible broadcast trees simultaneously, while requiring O(N²) messages to be exchanged between nodes. We compare our algorithm´s performance to the best-known centralized algorithm, and show that it constructs trees consuming, on average, only 18% more energy. We also consider the possibility of having multiple source nodes that can be used to broadcast the message and adapt our algorithm to compute energy-efficient broadcast trees with multiple source nodes. We observe a reduction in the amount of energy needed to form the broadcast tree that is linear in the number of source nodes.