Greedy drawings of triangulations

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Greedy drawings of triangulations
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
Added 30 Oct 2010
Updated 30 Oct 2010
Type Conference
Year 2008
Where SODA
Authors Raghavan Dhandapani
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