Hybrid通信网络中的近最短路径路由
Near-Shortest Path Routing in Hybrid Communication Networks
摘要：
混合网络，即，利用不同通信手段的网络变得越来越广泛。为了对这种网络进行理论研究，[Augustine et al.，SODA'20]引入了$\mathsf{HYBRID}$模型，该模型基于同步消息传递的概念，并使用两种根本不同的通信原理：本地模式，允许每个节点与本地通信图中的每个邻居每轮交换一条消息;以及全局模式，其中任何节点对都可以交换消息，但每轮只能进行很少的此类交换。以前对$\mathsf{HYBRID}$模型的研究中有相当大的一部分是围绕基本的通信原语和计算网络中的距离或最短路径进行的。在本文中，我们将这项研究扩展到一个相关的基本问题，计算紧凑的路由方案的近最短路径的本地通信图。我们证明，在这种情况下，本地通信图是一个单位盘图与$n$节点，实现在平面上，并没有无线电孔，我们可以确定性地计算路由方案，具有恒定的拉伸和使用标签和本地路由表的大小$O(\log n)$位在只有$O(\log n)$轮。
英文摘要：
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.
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