The Energy Complexity of Broadcast

Abstract

Energy is often the most constrained resource in networks of battery-powered 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 include:• The energy complexity of Broadcast in a multi-hop network is intimately 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, we need Ω(log n) and Ω(log 2 n) energy, respectively.• The energy lower bounds above can almost be achieved, given sufficient (Ω(n)) time. In the CD and No-CD models we can solve Broadcast using O( log n log log n log log log n ) energy and O(log 3 n) energy, respectively. • The complexity measures of Energy and Time are in conflict, and it is an open problem whether both can be minimized simultaneously. We give a tradeoff showing it is possible to be nearly optimal in both measures simultaneously. For any constant > 0, Broadcast can be solved in O(D 1+ log O(1/ ) n) time with O(log O(1/ ) n) energy, where D is the diameter of the network.

Fast and Resource Competitive Broadcast in Multi-channel Radio Networks

“…Classical results often rely on variants of the DECAY procedure [10], while recent ones (see, e.g., [11]- [14]) tend to employ more advanced techniques (such as network decomposition) to improve performance. Besides time complexity, energy cost has also been taken into consideration when building communication primitives (see, e.g., [1], [2], [15], [16]), but usually without assuming the existence of a jamming adversary.…”

“…We are now ready to prove part (2). Notice that E[Xu]/∆u = E[Xv]/∆v = α·|Q|/(RC) where α = w∈V (1−pw/C).…”

“…Moreover, allowing different actions to have different constant costs will not affect the results. 2 We say an event happens with high probability (w.h.p.) if the event occurs with probability at least 1−1/n c , for some tunable constant c ≥ 1.…”

Brief Announcement: Wake Up and Join Me! An Energy Efficient Algorithm for Maximal Matching in Radio Networks

“…Moreover, this has tended to be increasingly true as the devices have gotten smaller; see, for example, [3,10,13]. Motivated by these considerations, Chang et al [4] introduced a theoretical model of distributed computation in which each send or listen operation costs one unit of energy, but local computation is free. Over a sequence of discrete timesteps, nodes choose whether to sleep, listen, or send a message of (log ) bits.…”

“…In this model, Chang et al [4] presented a polylog-energy, polytime algorithm for the problem of one-to-all broadcast. A later paper, by Chang, Dani, Hayes and Pettie [5], gave a sub-polynomial energy, polynomial-time algorithm for the related problem of breadth-first search.…”