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Notes on Graph Cuts with Submodular Edge Weights

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons83994

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

http://pubman.mpdl.mpg.de/cone/persons/resource/persons83814

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

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Zitation

Jegelka, S., & Bilmes, J. (2009). Notes on Graph Cuts with Submodular Edge Weights. In NIPS 2009 Workshop on Discrete Optimization in Machine Learning: Submodularity, Sparsity & Polyhedra (DISCML) (pp. 1-6).


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-0013-C1DE-D
Zusammenfassung
Generalizing the cost in the standard min-cut problem to a submodular cost function immediately makes the problem harder. Not only do we prove NP hardness even for nonnegative submodular costs, but also show a lower bound of (|V |1/3) on the approximation factor for the (s, t) cut version of the problem. On the positive side, we propose and compare three approximation algorithms with an overall approximation factor of O(min|V |,p|E| log |V |) that appear to do well in practice.