Current flow models for matching signals on graphs assume that the cost of moving information between vertices is proportional to the shortest path along the graph. However, this approach is known to suffer from degeneracy and non-uniqueness. A common solution on continuous domains is to consider costs that scale quadratically in distance. Such approaches do not transfer well to the discrete case as current optimization tools are not suited for quadratic matching problems. I plan to leverage new approximation methods for similar problems, as well as standard linear programming formulations to provide a resolution to this problem.
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