Broadcasting Competitively against Adaptive Adversary in Multi-channel Radio Networks

Broadcasting in wireless networks is vulnerable to adversarial jamming. To thwart such behavior, \emph{resource competitive analysis} is proposed. In this framework, sending, listening, or jamming on one channel for one time slot costs one unit of energy. The adversary can employ arbitrary strategy to disrupt communication, but has a limited energy budget $T$. The honest nodes, on the other hand, aim to accomplish broadcast while spending only $o(T)$. Previous work has shown, in a $C$-channels network containing $n$ nodes, for large $T$ values, each node can receive the message in $\tilde{O}(T/C)$ time, while spending only $\tilde{O}(\sqrt{T/n})$ energy. However, these multi-channel algorithms only work for certain values of $n$ and $C$, and can only tolerate an oblivious adversary. In this work, we provide new upper and lower bounds for broadcasting in multi-channel radio networks, from the perspective of resource competitiveness. Our algorithms work for arbitrary $n,C$ values, require minimal prior knowledge, and can tolerate a powerful adaptive adversary. More specifically, in our algorithms, for large $T$ values, each node's runtime is $O(T/C)$, and each node's energy cost is $\tilde{O}(\sqrt{T/n})$. 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 (within a poly-log factor). Our technical contributions lie in using "epidemic broadcast" to achieve time efficiency and resource competitiveness, and employing coupling techniques in the analysis to handle the adaptivity of the adversary. At the lower bound side, we first derive a new energy complexity lower bound for 1-to-1 communication in the multi-channel setting, and then apply simulation and reduction arguments to obtain the desired result.