Euclidean Minimum Spanning Tree - Planar Realization

Planar Realization

The realization problem for Euclidean minimum spanning trees is stated as follows: Given a tree T = (V, E), find a location D(u) for each vertex uV so that T is a minimum spanning tree of D(u): u ∈ V, or determine that no such locations exist. Testing of the existence of a realization in the plane is NP-hard.

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    Probably nothing in the experience of the rank and file of workers causes more bitterness and envy than the realization which comes sooner or later to many of them that they are “stuck” and can go no further.
    Mary Barnett Gilson (1877–?)