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Cooperative Cuts: Graph Cuts with Submodular Edge Weights

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Jegelka,  S
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Bilmes,  J
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Jegelka, S., & Bilmes, J. (2010). Cooperative Cuts: Graph Cuts with Submodular Edge Weights. In 24th European Conference on Operational Research (EURO XXIV) (pp. 171).


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-BF60-1
Abstract
We introduce cooperative cut, a minimum cut problem whose cost is a submodular function on sets of edges: the cost of an edge that is added to a cut set depends on the edges in the set. Applications are e.g. in probabilistic graphical models and image processing. We prove NP hardness and a polynomial lower bound on the approximation factor, and upper bounds via four approximation algorithms based on different techniques. Our additional heuristics have attractive practical properties, e.g., to rely only on standard min-cut. Both our algorithms and heuristics appear to do well in practice.