2013/06/21 by Martin Nöllenburg, Nöllenburg, Martin, Roman Prutkin +1
Computer Science · #Computational Geometry (cs.CG) #FOS: Computer and information sciences #cs.CG
paper · pdf · doi:10.48550/arxiv.1306.5224
Expanded version of a paper to appear in the 21st European Symposium on Algorithms (ESA 2013). 24 pages, 20 figures
arxiv created 2013/06/21 · arxiv updated 2013/06/24
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 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.