Euclidean Greedy Drawings of Trees

  • Martin Nöllenburg
  • Roman Prutkin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8125)

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 s,t 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 Euclidean greedy embeddings in ℝ2 is known for certain graph classes such as 3-connected planar graphs. We completely characterize the trees that admit a greedy embedding in ℝ2. This answers a question by Angelini et al. (Graph Drawing 2009) and is a further step in characterizing the graphs that admit Euclidean greedy embeddings.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Martin Nöllenburg
    • 1
  • Roman Prutkin
    • 1
  1. 1.Institute of Theoretical InformaticsKarlsruhe Institute of TechnologyGermany

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