Packing plane spanning graphs with short edges in complete geometric graphs

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

Research output: Contribution to journalArticlepeer-review

Abstract

Given a set of points in the plane, we want to establish a connected spanning graph between these points, called connection network, that consists of several disjoint layers. Motivated by sensor networks, our goal is that each layer is connected, spanning, and plane. No edge in this connection network is too long in comparison to the length needed to obtain a spanning tree. We consider two different approaches. First we show an almost optimal centralized approach to extract two layers. Then we consider a distributed model in which each point can compute its adjacencies using only information about vertices at most a predefined distance away. We show a constant factor approximation with respect to the length of the longest edge in the graphs. In both cases the obtained layers are plane.

Original languageEnglish
Pages (from-to)1-15
Number of pages15
JournalComputational Geometry: Theory and Applications
Volume82
DOIs
Publication statusPublished - 2019 Sep

Keywords

  • Bottleneck edge
  • Geometric graphs
  • Graph packing
  • Minimum spanning tree
  • Plane graphs

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics

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