We consider the problem of routing a data packet through the visibility graph of a polygonal domain P with n vertices and h holes. We may preprocess P to obtain a label and a routing table for each vertex of P. Then, we must be able to route a data packet between any two vertices p and q of P, where each step must use only the label of the target node q and the routing table of the current node.

For any fixed $\epsilon >0$, we present a routing scheme that always achieves a routing path whose length exceeds the shortest path by a factor of at most $1+\epsilon$. The labels have $O(\log n)$ bits, and the routing tables are of size $O(({\epsilon }^{-1}+h)\log n)$. The preprocessing time is $O(n^2\log n)$. It can be improved to $O(n^2)$ for simple polygons.

我们考虑通过具有n个顶点和h个孔的多边形域P的可见性图来路由数据包的问题。我们可以进行预处理P获得标签和路由表的每个顶点P。然后，我们必须能够路由任意两个顶点之间的数据包p和q的P，其中每个步骤必须仅使用所述目标节点的标签q和当前节点的路由表。

对于任何固定 $\epsilon >0$，我们提出了一种路由方案，该方案始终可以实现一条长度超过最短路径最大为两倍的路由路径 $\mathrm{1个}+\epsilon$。标签有$Ø（\mathrm{日志}ñ）$ 位，并且路由表的大小 $Ø（（{\epsilon }^{-\mathrm{1个}}+H）\mathrm{日志}ñ）$。预处理时间是$Ø（{ñ}^2\mathrm{日志}ñ）$。可以改进为$Ø（{ñ}^2）$ 用于简单的多边形。