Euclidean Greedy Drawings of Trees [article]

Martin Nöllenburg, Roman Prutkin
2013 arXiv   pre-print
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 greedy embeddings in the Euclidean plane 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 R^2. This answers a
more » ... by Angelini et al. (Graph Drawing 2009) and is a further step in characterizing the graphs that admit Euclidean greedy embeddings.
arXiv:1306.5224v1 fatcat:fsy6br5yxnau5mtcjpljggnpp4