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Planar Bichromatic Bottleneck Spanning Trees

Authors A. Karim Abu-Affash, Sujoy Bhore, Paz Carmi, Joseph S. B. Mitchell

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Author Details

A. Karim Abu-Affash
  • Software Engineering Department, Shamoon College of Engineering, Beer-Sheva, Israel
Sujoy Bhore
  • Department of Computer Science, Ben-Gurion University, Beer-Sheva, Israel
Paz Carmi
  • Department of Computer Science, Ben-Gurion University, Beer-Sheva, Israel
Joseph S. B. Mitchell
  • Department of Applied Mathematics and Statistics, Stony Brook University, NY, USA

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A. Karim Abu-Affash, Sujoy Bhore, Paz Carmi, and Joseph S. B. Mitchell. Planar Bichromatic Bottleneck Spanning Trees. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 1:1-1:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


Given a set P of n red and blue points in the plane, a planar bichromatic spanning tree of P is a geometric spanning tree of P, such that each edge connects between a red and a blue point, and no two edges intersect. In the bottleneck planar bichromatic spanning tree problem, the goal is to find a planar bichromatic spanning tree T, such that the length of the longest edge in T is minimized. In this paper, we show that this problem is NP-hard for points in general position. Our main contribution is a polynomial-time (8√2)-approximation algorithm, by showing that any bichromatic spanning tree of bottleneck λ can be converted to a planar bichromatic spanning tree of bottleneck at most 8√2 λ.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Theory of computation → Design and analysis of algorithms
  • Approximation Algorithms
  • Bottleneck Spanning Tree
  • NP-Hardness


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