Near-Optimal Time-Energy Trade-Offs for Deterministic Leader Election

We consider the energy complexity of leader election problem in single-hop radio network model, where each device v has a unique identifier ID ( ) ∈{ 1, 2, ⋖ , N } . Energy is scarce resource for small battery-powered devices. For such devices, most often spent on communication, not computation. To approximate actual cost, an algorithm defined as maximum over all devices number time slots transmits or listens. Much progress been made understanding networks, but very little known about tradeoff between and energy. Chang et al. [STOC 2017] showed that optimal deterministic Θ (log log if can simultaneously transmit listen still leaving determining under any given constraint. Time–energy tradeoff: k ≥ we show among at n be elected deterministically O ċ 1+ε + 1/k listen, ε > 0 constant. This improves upon previous )-time )-energy by 2017]. provide lower bounds to time–energy our near-optimal. Dense instances: dense instances = ), design using only (1) (log* Jurdziński, Kutyłowski, Zatopiański [PODC 2002] (α ))-energy More specifically, \(\Theta (\max \lbrace \log \tfrac{N}{n}\rbrace)\) cannot it \(Θ listen.