Token traversal in ad hoc wireless networks via implicit carrier sensing

Abstract

Communication problems in ad hoc wireless networks have been already widely studied under the SINR model, but a vast majority of results concern networks with constraints on connectivity, so called strongly-connected networks. In such networks, connectivity is defined based on highly reliable links, that is, where both ends are located far closer from their transmission boundaries. What happens if the network is not strongly-connected, e.g., it contains some long but still viable “shortcut links” connecting transmission boundaries? It is known that even a single broadcast in such ad hoc weakly-connected networks with uniform transmission powers requires $\mathrm{\Omega }(n)$ communication rounds, where n is the number of nodes in the network. The best up-to-date (randomized) distributed algorithm, designed by Daum et al. [1], accomplishes broadcast task in $O(n{\log }^{2}n)$ communication rounds with high probability.

In this work, inspired by the work on broadcasting, we show a novel deterministic distributed implementation of token traversal — a fundamental tool in distributed systems — in the SINR model with uniform transmission powers and no restriction on connectivity. We show that it is efficient even in a very harsh model of weakly-connected networks without GPS, carrier sensing and other helping features. We apply this method to span a traversal tree and accomplish broadcast in $O(n\log N)$ communication rounds, deterministically, provided nodes are equipped with unique IDs in the range $[1,N]$ for some integer $N\ge n$. This result implies an $O(n\log n)$-round randomized solution that does not require IDs, which improves the result from [1]. The lower bound $\mathrm{\Omega }(n\log N)$ for deterministic algorithms proved in our work shows that our result is tight without randomization. Our implementation of token traversal routine, efficient in terms of time and memory, is based on a novel implicit algorithmic carrier sensing method and a new type of selectors, which might be of independent interest and applicable to other communication tasks in distributed ad hoc setting.