Solomon and Elkin (SIAM J Discret Math 28(3):1173–1198, 2014) constructed a shortcutting scheme for weighted trees which results in a 1-spanner for the tree metric induced by the input tree. The spanner has logarithmic lightness, logarithmic diameter, a linear number of edges and bounded degree (provided the input tree has bounded degree). This spanner has been applied in a series of papers devoted to designing bounded degree, low-diameter, low-weight \((1+\epsilon )\)-spanners in Euclidean and doubling metrics. In this paper, we present a simple local routing algorithm for this tree metric spanner. The algorithm has a routing ratio of 1, is guaranteed to terminate after \(O(\log n)\) hops and requires \(O(\varDelta \log n)\) bits of storage per vertex where \(\varDelta \) is the maximum degree of the tree on which the spanner is constructed. This local routing algorithm can be adapted to a local routing algorithm for a doubling metric spanner which makes use of the shortcutting scheme.

Solomon 和 Elkin (SIAM J Discret Math 28(3):1173–1198, 2014) 为加权树构建了一个捷径方案，这导致输入树诱导的树度量的 1-spanner。扳手具有对数亮度、对数直径、线性边数和有界度数（假设输入树具有有界度数）。该扳手已在一系列致力于设计有界度、低直径、低权重\((1+\epsilon )\)欧几里得和加倍度量中的扳手的论文中得到应用。在本文中，我们为该树度量生成器提出了一种简单的本地路由算法。该算法的路由比为 1，保证在\(O(\log n)\)跳后终止，并且每个顶点需要\(O(\varDelta \log n)\)位存储，其中\(\varDelta \)是构建扳手的树的最大度数。该本地路由算法可以适用于使用捷径方案的双度量生成器的本地路由算法。