Information exchange with collision detection on multiple channels

Abstract

Information exchange is a fundamental communication primitive in radio networks. We study this problem in multi-channel single-hop networks. In particular, given $k$ pieces of information, initially stored in $k$ nodes respectively, the task is to broadcast these information pieces to the entire network via a set of $\mathcal {F}$ channels. We develop efficient distributed algorithms for this task for the scenario where both the identities and the number $k$ of the initial information holders are unknown to the participating nodes. Assuming nodes with collision detection, we present an efficient randomized algorithm for unrestricted information exchange, where multiple information items can be combined into a single message. The algorithm disseminates all the information items within $O(\frac{k}{\mathcal {F}}+\mathcal {F}\log ^2n)$ timeslots with high probability. To the best of our knowledge, this is the first algorithm that breaks the $\varOmega (k)$ lower bound for unrestricted information exchange if only a single channel is available. This result establishes the superiority of multiple channels for the task of unrestricted information exchange. Moreover, for restricted information exchange, where each message can carry only one information item, we devise a randomized algorithm that completes the task in $O(k+\frac{\log ^2n}{\mathcal {F}}+\log n)$ timeslots. When $k$ is large, both algorithms are asymptotically optimal, as they can reach the trivial lower bounds of $\varOmega (\frac{k}{\mathcal {F}})$ and $\varOmega (k)$ for unrestricted and restricted information exchange, respectively.