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Load balancing by network curvature control

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It is argued that traffic congestion in computer network is a sequel of the combination of greedy routing and negative curvature. Negative curvature here is to be interpreted in the sense of Gromov, which roughly means that the Internet can be approximated by a Riemannian manifold of negative curvature. We will propose a general conjecture that the point of heaviest congestion in a negatively curved network is the center of mass of the network, defined as a point relative to which the inertia of the network is minimum. Next, if negative curvature implies congestion, it turns out that most elementary techniques will be ineffective unless they manage to go around the fundamental negative curvature limitation. The proposed curvature based load balancing consists in running the so-called Yamabe flow algorithm—instrumental in the proof of the Poincare conjecture—to assign link weights so that the resulting network has uniform positive curvature, assuming that an Euler characteristic obstruction vanishes. Then doing the routing on the modified network with controlled curvature and mapping the routing back to the original network provides nearly uniform traffic load.

This talk is part of the CUED Control Group Seminars series.

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