Some Results on Greedy Embeddings in Metric Spaces
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Leighton_Some results on greedy.pdf
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218.21 KB
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Author(s)
Moitra, Ankur
Leighton, Frank Thomson
Date Issued
October 2009
Journal
Discrete & Computational Geometry
Publisher
Springer Science + Business Media B.V.
Citation
Leighton, Tom, and Ankur Moitra. “Some Results on Greedy Embeddings in Metric Spaces.” Discrete & Computational Geometry 44, no. 3 (October 20, 2010): 686-705.
Version
Author's final manuscript
Abstract
Geographic Routing is a family of routing algorithms that uses geographic point locations as addresses for the purposes of routing. Such routing algorithms have proven to be both simple to implement and heuristically effective when applied to wireless sensor networks. Greedy Routing is a natural abstraction of this model in which nodes are assigned virtual coordinates in a metric space, and these coordinates are used to perform point-to-point routing.
Here we resolve a conjecture of Papadimitriou and Ratajczak that every 3-connected planar graph admits a greedy embedding into the Euclidean plane. This immediately implies that all 3-connected graphs that exclude K 3,3 as a minor admit a greedy embedding into the Euclidean plane. We also prove a combinatorial condition that guarantees nonembeddability. We use this result to construct graphs that can be greedily embedded into the Euclidean plane, but for which no spanning tree admits such an embedding.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1007/s00454-009-9227-6
