eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2016-12-07
9:1
9:12
10.4230/LIPIcs.ISAAC.2016.9
article
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
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol064-isaac2016/LIPIcs.ISAAC.2016.9/LIPIcs.ISAAC.2016.9.pdf
Geometric Graphs
Graph Packing
Plane Graphs
Minimum Spanning Tree
Bottleneck Edge