Packing short plane spanning trees in complete geometric graphs

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

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.

Original languageEnglish
Title of host publication27th International Symposium on Algorithms and Computation, ISAAC 2016
EditorsSeok-Hee Hong
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages9.1-9.12
ISBN (Electronic)9783959770262
DOIs
Publication statusPublished - 2016 Dec 1
Event27th International Symposium on Algorithms and Computation, ISAAC 2016 - Sydney, Australia
Duration: 2016 Dec 122016 Dec 14

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume64
ISSN (Print)1868-8969

Other

Other27th International Symposium on Algorithms and Computation, ISAAC 2016
CountryAustralia
CitySydney
Period16/12/1216/12/14

Keywords

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

ASJC Scopus subject areas

  • Software

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  • Cite this

    Aichholzer, O., Hackl, T., Korman, M., Pilz, A., Rote, G., Van Renssen, A., Roeloffzen, M., & Vogtenhuber, B. (2016). Packing short plane spanning trees in complete geometric graphs. In S-H. Hong (Ed.), 27th International Symposium on Algorithms and Computation, ISAAC 2016 (pp. 9.1-9.12). (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 64). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ISAAC.2016.9