Directional Routing via Generalized st-Numberings

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Directional Routing via Generalized st-Numberings
We present a mathematical model for network routing based on generating paths in a consistent direction. Our development is based on an algebraic and geometric framework for defining a directional coordinate system for real vector spaces. Our model, which generalizes graph st-numberings, is based on mapping the nodes of a network to points in multidimensional space and ensures that the paths generated in different directions from the same source are node-disjoint. Such directional embeddings encode the global disjoint path structure with very simple local information. We prove that all 3-connected graphs have 3-directional embeddings in the plane so that each node outside a set of extreme nodes has a neighbor in each of the three directional regions defined in the plane. We conjecture that the result generalizes to k-connected graphs. We also show that a directed acyclic graph (dag) that is k-connected to a set of sinks has a k-directional embedding in (k - 1)-space with the sink set a...
Fred S. Annexstein, Kenneth A. Berman
Added 19 Dec 2010
Updated 19 Dec 2010
Type Journal
Year 2000
Authors Fred S. Annexstein, Kenneth A. Berman
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