Nöllenburg, M., & Prutkin, R. (2017). Euclidean Greedy Drawings of Trees. Discrete and Computational Geometry, 58(3), 543–579. https://doi.org/10.1007/s00454-017-9913-8
E192-01 - Forschungsbereich Algorithms and Complexity
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Journal:
Discrete and Computational Geometry
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ISSN:
0179-5376
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Date (published):
Oct-2017
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Number of Pages:
37
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Publisher:
SPRINGER
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Peer reviewed:
Yes
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Keywords:
Theoretical Computer Science; Computational Theory and Mathematics; Discrete Mathematics and Combinatorics; Geometry and Topology; Greedy drawings; Tree drawings; Greedy routing
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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. (Networks 59(3):267-274, 2012) and is a further step in characterizing the graphs that admit Euclidean greedy embeddings.
