## Abstract

Every pair of points lying on a polygonal path P in the plane has a detour associated with it, which is the ratio between their distance along the path and their Euclidean distance. Given a set S of points along the path, this information can be encoded in a weighted complete graph on S. Among all spanning trees on this graph, a bottleneck spanning tree is one whose maximum edge weight is minimum. We refer to such a tree as a bottleneck detour tree of S. In other words, a bottleneck detour tree of S is a spanning tree in which the maximum detour (with respect to the original path) between pairs of adjacent points is minimum. We show how to find a bottleneck detour tree in expected O(nlog ^{3} n+m) time, where P consists of m edges and |S|=n.

Original language | English |
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Pages (from-to) | 30-36 |

Number of pages | 7 |

Journal | Computational Geometry: Theory and Applications |

Volume | 79 |

DOIs | |

State | Published - 1 Feb 2019 |

## Keywords

- Bottleneck spanning tree
- Detour
- Polygonal path
- Randomized algorithm