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Drawing a rooted tree as a rooted y-monotone minimum spanning tree

机译：将一个扎根的树绘制为rooted y-monotone最小生成树

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摘要

Given a set P of points in the plane, and a point r is an element of P identified as the root of P, the rooted y-Monotone Minimum Spanning Tree (rooted y-MMST) of P is the connected spanning geometric graph of P in which all the vertices are connected to the root by some y-monotone path and the sum of the Euclidean lengths of its edges is the minimum. We give a linear-time algorithm that draws any rooted tree as a rooted y-MMST. A corollary of the previous sentence is that for every natural number M there exists a rooted y-MMST of maximum degree M. We also show that there exist n-node rooted trees for which any grid drawing as a rooted y-MMST requires a grid of area exponential in n. (C) 2020 Elsevier B.V. All rights reserved.
机译：给定飞机中的点P，并且点R是识别为p的根的p的元素，P的根为y-monotone最小生成树（rooted y-mmst）是p的连接跨越几何图其中所有顶点通过一些Y-单调路径连接到根，并且其边缘的欧几里德长度的总和是最小的。我们提供了一个线性时算法，将任何rooted树绘制为rooted y-mmst。前一句的推论是，对于每个自然数M，存在最大程度的根源Y-MMST。我们还表明存在n节点rooted树，其中任何网格绘制为根y-mmst需要网格。在n中的区域指数（c）2020 Elsevier B.v.保留所有权利。

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