Energy-efficient and delay-constrained broadcast in time-varying energy-demand graphs

In this paper, we study the minimum energy broadcast problem in time-varying graphs (TVGs), which are a very useful high level abstraction for studying highly dynamic wireless networks. To this end, we first incorporate a channel model, called energy-demand functions, to the current TVGs, namely time-varying energy-demand graphs (TVEGs). Based on this model, we formulate the problem: given a TVEG, what is the optimal schedule (i.e., Which nodes should forward a packet in what times and at what power levels) to minimize the energy consumption of the broadcast? We prove the problem to be NP-hard and o(log N) in approximable. It is a challenge to find a solution for this problem on continuous time. Fortunately, we prove that the problem on continuous time is equivalent to the problem on certain discrete time points, called discrete time set (DTS). Based on this property, we propose polynomial time solutions for this problem with different channel models, and evaluate the performance of these methods from real-life contact traces.