Euclidean Greedy Drawings of Trees
Computational Geometry
2013-06-24 v1
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 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 question by Angelini et al. (Graph Drawing 2009) and is a further step in characterizing the graphs that admit Euclidean greedy embeddings.
Keywords
Cite
@article{arxiv.1306.5224,
title = {Euclidean Greedy Drawings of Trees},
author = {Martin Nöllenburg and Roman Prutkin},
journal= {arXiv preprint arXiv:1306.5224},
year = {2013}
}
Comments
Expanded version of a paper to appear in the 21st European Symposium on Algorithms (ESA 2013). 24 pages, 20 figures