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Discrete & Computational Geometry

, Volume 58, Issue 3, pp 543–579 | Cite as

Euclidean Greedy Drawings of Trees

  • Martin Nöllenburg
  • Roman Prutkin
Article

Abstract

Greedy embedding (or drawing) is a simple and efficient strategy to route messages in wireless sensor networks. For each source-destination pair of nodes st in a greedy embedding there is always a neighbor u of s that is closer to t according to some distance metric. The existence of greedy embeddings in the Euclidean plane \({\mathbb {R}}^2\) is known for certain graph classes such as 3-connected planar graphs. We completely characterize the trees that admit a greedy embedding in \({\mathbb {R}}^2\). This answers a question by Angelini et al. (Networks 59(3):267–274, 2012) and is a further step in characterizing the graphs that admit Euclidean greedy embeddings.

Keywords

Greedy drawings Tree drawings Greedy routing 

Mathematics Subject Classification

05C05 05C10 68R10 

Notes

Acknowledgements

M.N. received financial support by the “Concept for the Future” of KIT within the framework of the “German Excellence Initiative”. R.P. was supported by the German Research Foundation (DFG) within the Research Training Group GRK 1194 “Self-Organizing Sensor-Actuator Networks”.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Algorithms and Complexity GroupTU WienViennaAustria
  2. 2.Institute of Theoretical InformaticsKarlsruhe Institute of TechnologyKarlsruheGermany

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