Drawing a Rooted Tree as a Rooted y-Monotone Minimum Spanning Tree
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Given a rooted point set P, the rooted y-Monotone Minimum Spanning Tree (rooted y-MMST) of P is the 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 show that the maximum degree of a rooted y-MMST is not bounded by a constant number. We give a linear time algorithm that draws any rooted tree as a rooted y-MMST and also show that there exist rooted trees that can be drawn as rooted y-MMSTs only in a grid of exponential area.
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