Hybrid networks, i.e., networks that leverage different means of communication, become ever more widespread. To allow theoretical study of such networks, [Augustine et al., SODA'20] introduced the $\mathsf{HYBRID}$ model, which is based on the concept of synchronous message passing and uses two fundamentally different principles of communication: a local mode, which allows every node to exchange one message per round with each neighbor in a local communication graph; and a global mode where any pair of nodes can exchange messages, but only few such exchanges can take place per round. A sizable portion of the previous research for the $\mathsf{HYBRID}$ model revolves around basic communication primitives and computing distances or shortest paths in networks. In this paper, we extend this study to a related fundamental problem of computing compact routing schemes for near-shortest paths in the local communication graph. We demonstrate that, for the case where the local communication graph is a unit-disc graph with $n$ nodes that is realized in the plane and has no radio holes, we can deterministically compute a routing scheme that has constant stretch and uses labels and local routing tables of size $O(\log n)$ bits in only $O(\log n)$ rounds.

翻译：利用不同通信手段的混合网络,即利用不同通信手段的网络,越来越普遍。为了允许对这些网络进行理论研究,[Augustine 等人, SODA'20] 引入了美元模型,该模型以同步传递信息的概念为基础,并使用两种根本不同的通信原则:一种本地模式,允许每个节点在本地通信图中与每个邻居每圆交换一条信息;一种全球模式,任何对节点都可以交换信息,但这种交换每轮只能进行。以前对美元和美元进行的一项研究中的一部分是围绕基本通信原始和计算距离或网络中最短路径进行的。在本文中,我们将这项研究扩大到一个相关的根本问题,即为本地通信图中的近距离路径计算紧凑的紧凑路线计划。我们证明,对于本地通信图是单位-偏差图,只有美元节点才能进行这种交流。对于飞机上实现的无射线洞,我们只能用美元对美元进行固定的路径图表进行固定式的固定式拼凑。