Multi-commodity Allocation for Dynamic Demands Using PageRank Vectors

We consider a variant of the contact process concerning multi-commodity allocation on networks. In this process, the demands for several types of commodities are initially given at some specified vertices and then the demands spread interactively on a contact graph. To allocate supplies in such a dynamic setting, we use a modified version of PageRank vectors, called Kronecker PageRank, to identify vertices for shipping supplies. We analyze both the situation that the demand distribution evolves mostly in clusters around the initial vertices and the case that the demands spread to the whole network. We establish sharp upper bounds for the probability that the demands are satisfied as a function of PageRank vectors.

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