Given a set of well-formed terminal pairs on the external face of an undirected planar graph with unit edge weights, we give a linear-time algorithm for computing the union of non-crossing shortest paths joining each terminal pair, where well-formed means that such a set of non-crossing paths exists. This allows us to compute distances between each terminal pair, within the same time bound. We also give a novel concept of incremental shortest path subgraph of a planar graph, i.e., a partition of the planar embedding in subregions that preserve distances, that can be of interest itself.
翻译：鉴于外部外观有一套设计完善的配对配对,配有单位边缘重量的无方向平面图,我们用线性时间算法计算非交叉的最短路径结合每个配对的配对,在这种配对配对配对配对配对配对配对配对配对配对配对配对配对配对配对配对配对配对配对配对配对配对配对配对配对配对配对配对配对配对配对配对配对配对配对配对配对配对配对配对配对,这样可以计算每对配对配对配对配对配对配对的距离,在同时约束内计算每对配对配对配对配对配对的距离。我们还给出了一个新概念,即平面图的递增程最短路径子图,即将平面嵌入的平面分隔在能够保持距离的次区域,这本身可能有意义。
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