Towards Minimizing k-Submodular Functions

  • Anna Huber
  • Vladimir Kolmogorov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7422)


In this paper we investigate k-submodular functions. This natural family of discrete functions includes submodular and bisubmodular functions as the special cases k = 1 and k = 2 respectively.

In particular we generalize the known Min-Max-Theorem for submodular and bisubmodular functions. This theorem asserts that the minimum of the (bi)submodular function can be found by solving a maximization problem over a (bi)submodular polyhedron. We define a k-submodular polyhedron, prove a Min-Max-Theorem for k-submodular functions, and give a greedy algorithm to construct the vertices of the polyhedron.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Anna Huber
    • 1
  • Vladimir Kolmogorov
    • 2
  1. 1.School of Engineering and Computing SciencesDurham UniversityDurhamUK
  2. 2.Institute of Science and Technology AustriaKlosterneuburgAustria

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