Approximating Longest Spanning Tree with Neighborhoods
We study the following maximization problem in the Euclidean plane: Given a collection of neighborhoods (polygonal regions) in the plane, the goal is to select a point in each neighborhood so that the longest spanning tree on selected points has maximum length. It is not known whether or not this problem is NP-hard. We present an approximation algorithm with ratio 0.548 for this problem. This improves the previous best known ratio of 0.511.
The presented algorithm takes linear time after computing a diameter. Even though our algorithm itself is fairly simple, its analysis is rather involved. In some part we deal with a minimization problem with multiple variables. We use a sequence of geometric transformations to reduce the number of variables and simplify the analysis.
Euclidean maximum spanning tree
spanning tree with neighborhoods
approximation algorithms
Theory of computation~Computational geometry
Theory of computation~Approximation algorithms analysis
7:1-7:11
Regular Paper
Supported by NSERC.
Ahmad
Biniaz
Ahmad Biniaz
School of Computer Science, University of Windsor, Canada
https://cglab.ca/~biniaz/
10.4230/LIPIcs.ISAAC.2021.7
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Ahmad Biniaz
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