Discrete & Computational Geometry

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

Euclidean Greedy Drawings of Trees

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 

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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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