eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-30
7:1
7:11
10.4230/LIPIcs.ISAAC.2021.7
article
Approximating Longest Spanning Tree with Neighborhoods
Biniaz, Ahmad
1
School of Computer Science, University of Windsor, Canada
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol212-isaac2021/LIPIcs.ISAAC.2021.7/LIPIcs.ISAAC.2021.7.pdf
Euclidean maximum spanning tree
spanning tree with neighborhoods
approximation algorithms