Some Results on Greedy Embeddings in Metric Spaces

13 years 10 months ago

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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 ural 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 K3,3 as a minor admit a greedy embedding into the Euclidean plane. Additionally, we provide the ﬁrst non-trivial examples of graphs that admit no such embedding. These structural results provide eﬃciently veriﬁable certiﬁcates that a graph admits a greedy embedding or that a graph admits no greedy embedding into the Euclidean ...

Ankur Moitra, Tom Leighton

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