Images of natural systems may represent patterns of network-like structure, which could reveal important information about the topological properties of the underlying subject. However, the image itself does not automatically provide a formal …

We present a model for finding optimal multi-commodity flows on networks based on optimal transport theory. The model relies on solving a dynamical system of equations. We prove that its stationary solution is equivalent to the solution of an …

Optimizing traffic on a network is a relevant problem in situations where traffic congestion has a big impact on transmission performance. This can be formalized as a computationally-hard constrained optimization problem where interactions are non-local and a global optimization is required.

Routing optimization is a relevant problem in many contexts. Solving directly this type of optimization problem is often computationally unfeasible. Recent studies suggest that one can instead turn this problem into one of solving a dynamical system …

We present a message-passing algorithm to solve the edge disjoint path problem (EDP) on graphs incorporating under a unique framework both traffic optimization and path length minimization. The min-sum equations for this problem present an …

A localized method to distribute paths on random graphs is devised, aimed at finding the shortest paths between given source/destination pairs while avoiding path overlaps at nodes. We propose a method based on message-passing techniques to process …

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