Bottleneck detour tree of points on a path

Greg Aloupis, Paz Carmi, Lilach Chaitman-Yerushalmi, Matthew J. Katz, Stefan Langerman

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)30-36
Number of pages7
JournalComputational Geometry: Theory and Applications
StatePublished - 1 Feb 2019


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

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics


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