Greedy drawings of triangulations

13 years 5 months ago

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Greedy Routing is a class of routing algorithms in which the packets are forwarded in a manner that reduces the distance to the destination at every step. In an attempt to provide theoretical guarantees for a class of greedy routing algorithms, Papadimitriou and Ratajczak [PR05] came up with the following conjecture: Any 3-connected planar graph can be drawn in the plane such that for every pair of vertices s and t a distance decreasing path can be found. A path s = v1, v2, ..., vk = t in a drawing is said to be distance decreasing if vi t < vi-1 - t , 2 i k where . . . denotes the Euclidean distance. We settle this conjecture in the affirmative for the case of triangulations. A partitioning of the edges of a triangulation G into 3 trees, called the realizer of G, was first developed by Walter Schnyder who also gave a drawing algorithm based on this. We generalize Schnyder's algorithm to obtain a whole class of drawings of any given triangulation G. We show, using the Knaste...

Raghavan Dhandapani

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