Efficient and competitive broadcast in multi-channel radio networks

Abstract

Consider a single-hop, multi-channel, synchronous radio network in which a source node needs to disseminate a message to all other n−1 nodes. An adversary called Eve, which captures environmental noise and potentially malicious interference, aims to disrupt this process via jamming. Assume sending, listening, or jamming on one channel for one time slot costs one unit of energy. The question is, if Eve spends T units of energy on jamming, can we devise broadcast algorithms in which each node's cost is o(T)? Previous results show such resource competitive algorithms do exist in the single-channel setting: for large T values, each node can receive the message within O(T) time slots while spending only O˜(T/n) energy.In this work, we devise new broadcast algorithms and show that the existence of multiple channels allows faster message dissemination while preserving resource competitiveness. Specifically, if C channels are available, for large T values, our algorithms guarantee each node's runtime is O(T/C), and each node's energy cost is O˜(T/n). Moreover, our algorithms require minimal prior knowledge and allow Eve to be adaptive. Our technical contributions lie in using “epidemic broadcast” in algorithm design to achieve time efficiency and resource competitiveness, and employing coupling techniques in the analysis to handle the adaptivity of the adversary.We also complement algorithmic results with lower bounds, proving both the time complexity and the energy complexity of our algorithms are optimal or near-optimal. In particular, to obtain the lower bound on resource competitiveness, we first prove a new lower bound showing any multi-channel 1-to-1 communication algorithm succeeding with constant probability incurs expected cost of at least Ω(T); then, via simulation and reduction arguments, we show for the broadcast problem, some node incurs a cost of at least Ω(T/n), even in the multi-channel setting.