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In this paper, the authors address the problem of scalable and load balanced routing for wireless sensor networks. Motivated by the analog of the continuous setting that geodesic routing on a sphere gives perfect load balancing, they embed sensor nodes on a convex polyhedron in 3D and use greedy routing to deliver messages between any pair of nodes with guaranteed success. This embedding is known to exist by the Koebe-Andreev-Thurston Theorem for any 3-connected planar graphs. In their paper they use Ricci flow to develop a distributed algorithm to compute this embedding. Further, such an embedding is not unique and differ by one another with a Mobius transformation.
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