(Near) optimal resource-competitive broadcast with jamming

We consider the problem of broadcasting a message from a sender to n ≥ 1 receivers in a time-slotted, single-hop, wireless network with a single communication channel. Sending and listening dominate the energy usage of small wireless devices and this is abstracted as a unit cost per time slot. A jamming adversary exists who can disrupt the channel at unit cost per time slot, and aims to prevent the transmission of the message. Let T be the number of slots jammed by the adversary. Our goal is to design algorithms whose cost is resource-competitive, that is, whose per-device cost is a function, preferably o(T), of the adversary's cost. Devices must work with limited knowledge. The values n, T, and the adversary's jamming strategy are unknown. For 1-to-1 communication, we provide an algorithm with an expected cost of O(√Tln(1/∈) +ln(1/e)), which succeeds with probability at least 1 - ∈ for any tunable parameter ∈ > 0. For 1-to-n broadcast, we provide a very different algorithm that succeeds with high probability and yields an expected cost per device of O(√/nlog⁴ T + log⁶ n). Therefore, the bigger the system, the better advantage achieved over the adversary! We complement our upper bounds with tight or nearly tight lower bounds. We prove that any 1-to-1 communication algorithm with constant probability of success has expected costΩ(√T). For 1-ton broadcast we show that some node has cost Ω(√T/n). Finally, we consider a more powerful adversary that can spoof messages from the receiver, rather than just jam the channel. We prove that any 1-to-1 communication algorithm in this model has expected cost Ω(T^ℓ-1), where ℓ = 1+2 √5/2 is the golden ratio. This matches an earlier upper bound of King, Saia, and Young.