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arXiv · 2004.08854

Planar Bichromatic Bottleneck Spanning Trees

A. Karim Abu-Affash·Sujoy Bhore·Paz Carmi·Joseph S. B. Mitchell
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Abstract

Given a set $P$ of $n$ red and blue points in the plane, a \emph{planar bichromatic spanning tree} of $P$ is a 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. Moreover, we present a polynomial-time $(8\sqrt{2})$-approximation algorithm, by showing that any bichromatic spanning tree of bottleneck $\lambda$ can be converted to a planar bichromatic spanning tree of bottleneck at most $8\sqrt{2}\lambda$.

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A. Karim Abu-Affash, Sujoy Bhore, Paz Carmi, Joseph S. B. Mitchell. 2020-04-19. Planar Bichromatic Bottleneck Spanning Trees. https://arxiv.org/abs/2004.08854

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