Computing the Maximum Detour and Spanning Ratio of Planar Paths, Trees, and Cycles

@inproceedings{Langerman2002ComputingTM,
  title={Computing the Maximum Detour and Spanning Ratio of Planar Paths, Trees, and Cycles},
  author={Stefan Langerman and Pat Morin and Michael A. Soss},
  booktitle={STACS},
  year={2002}
}
The maximum detour and spanning ratio of an embedded graph G are values that measure how well G approximates Euclidean space and the complete Euclidean graph, respectively. In this paper we describe O(n logn) time algorithms for computing the maximum detour and spanning ratio of a planar polygonal path. These algorithms solve open problems posed in at least two previous works [5,10]. We also generalize these algorithms to obtain O(n log n) time algorithms for computing the maximum detour and… CONTINUE READING

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