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.

在SINR模型下，已经对ad hoc无线网络中的通信问题进行了广泛研究，但是绝大多数结果都涉及到对连接有限制的网络，即所谓的强连接网络。在这样的网络中，连接是基于高度可靠的链路定义的，也就是说，两端都位于距离其传输边界更近的位置。如果网络连接不牢固（例如，它包含一些长但仍可行的连接传输边界的“捷径链接”）会发生什么情况？众所周知，即使是在这种ad hoc弱连接网络中以均匀的发射功率进行的单个广播也需要$\mathrm{\Omega }（ñ）$通信回合，其中n是网络中的节点数。由Daum等人设计的最佳最新（随机）分布式算法。[1]，完成广播任务$Ø（ñ{\mathrm{日志}}^2ñ）$ 交流机会很高。

在这项工作中，受广播工作的启发，我们展示了SINR模型中具有遍历传输能力且对连接没有限制的令牌遍历（分布式系统中的基本工具）的新颖确定性分布式实现。我们证明，即使在没有GPS，载波侦听和其他帮助功能的弱连接网络的非常苛刻的模型中，该方法也是有效的。我们将这种方法应用于遍历遍历树并完成广播$Ø（ñ\mathrm{日志}ñ）$ 确定性地进行通信回合，前提是节点配备了范围内的唯一ID $[\mathrm{1个}，ñ]$ 对于一些整数 $ñ\ge ñ$。这个结果意味着$Ø（ñ\mathrm{日志}ñ）$不需要ID的全面随机解决方案，可提高[1]的结果。下界$\mathrm{\Omega }（ñ\mathrm{日志}ñ）$在我们的工作中证明的确定性算法表明，我们的结果是紧密的，没有随机化。我们在时间和内存方面高效的令牌遍历例程的实现是基于一种新颖的隐式算法载波侦听方法和一种新型的选择器，它们可能具有独立的意义，并适用于分布式ad hoc设置中的其他通信任务。