Computing Geometric Minimum-Dilation Graphs Is NP-Hard

@inproceedings{Klein2006ComputingGM,
  title={Computing Geometric Minimum-Dilation Graphs Is NP-Hard},
  author={Rolf Klein and Martin Kutz},
  booktitle={Graph Drawing},
  year={2006}
}
Consider a geometric graph G, drawn with straight lines in the plane. For every pair a, b of vertices of G, we compare the shortestpath distance between a and b in G (with Euclidean edge lengths) to their actual Euclidean distance in the plane. The worst-case ratio of these two values, for all pairs of vertices, is called the vertex-to-vertex dilation of G. We prove that computing a minimum-dilation graph that connects a given n-point set in the plane, using not more than a given number m of… CONTINUE READING
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