Packing Short Plane Spanning Trees in Complete Geometric Graphs

Aichholzer, Oswin; Hackl, Thomas; Korman, Matias; Pilz, Alexander; Rote, Günter; van Renssen, André; Roeloffzen, Marcel; Vogtenhuber, Birgit

doi:10.4230/LIPIcs.ISAAC.2016.9

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Document Identifiers

DOI: 10.4230/LIPIcs.ISAAC.2016.9
URN: urn:nbn:de:0030-drops-67823

Author Details

Oswin Aichholzer

Thomas Hackl

Matias Korman

Alexander Pilz

Günter Rote

André van Renssen

Marcel Roeloffzen

Birgit Vogtenhuber

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Oswin Aichholzer, Thomas Hackl, Matias Korman, Alexander Pilz, Günter Rote, André van Renssen, Marcel Roeloffzen, and Birgit Vogtenhuber. Packing Short Plane Spanning Trees in Complete Geometric Graphs. In 27th International Symposium on Algorithms and Computation (ISAAC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 64, pp. 9:1-9:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.ISAAC.2016.9

Abstract

Given a set of points in the plane, we want to establish a connection network between these points that consists of several disjoint layers. Motivated by sensor networks, we want that each layer is spanning and plane, and that no edge is very long (when compared to the minimum length needed to obtain a spanning graph). We consider two different approaches: first we show an almost optimal centralized approach to extract two trees. Then we show a constant factor approximation for a distributed model in which each point can compute its adjacencies using only local information. This second approach may create cycles, but maintains planarity.

Keywords

Geometric Graphs
Graph Packing
Plane Graphs
Minimum Spanning Tree
Bottleneck Edge

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References

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