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Bottleneck Detour Tree of Points on a Path

par Aloupis, Greg ;Carmi, Paz;Chaitman-Yerushalmi, Lilach;Katz, Matthew M.J.;Langerman, Stefan
Référence Computational geometry
Publication Publié, 2019-02-01

Article révisé par les pairs

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Résumé :

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