The Energy Complexity of Broadcast

Energy is often the most constrained resource in networks of batterypowered devices, and as devices become smaller, they spend a larger fraction of their energy on communication (transceiver usage) not computation. As an imperfect proxy for true energy usage, we define energy complexity to be the number of time slots a device transmits/listens; idle time and computation are free. In this paper we investigate the energy complexity of fundamental communication primitives such as Broadcast in multi-hop radio networks. We consider models with collision detection (CD) and without (No-CD), as well as both randomized and deterministic algorithms. Some take-away messages from this work are as follows. Time lower bounds imply energy lower bounds. The energy complexity of Broadcast in a multi-hop network is connected to the time complexity of LeaderElection in a single-hop (clique) network. Many existing lower bounds on time complexity immediately transfer to energy complexity. For example, in the CD and No-CD models, Broadcast requires Ω(logn) and Ω(log2 n) energy, respectively, w.h.p. Energy- and time-efficient broadcasting. It requires Ω(D) time to solve Broadcast even allowing unlimited energy budget, where D is the diameter of the network. The complexity measures of energy and time are in conflict, and it is an open problem whether both can be minimized simultaneously. We show that it is possible to achieve near optimality in time complexity with only poly logn energy cost. For any constant ε > 0, Broadcast can be solved in O(D1+ε logO(1/ε) n) time with O(logO(1/ε) n) energy.