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. © 2012 Springer-Verlag.
CITATION STYLE
Huber, A., & Kolmogorov, V. (2012). Towards minimizing k-submodular functions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7422 LNCS, pp. 451–462). https://doi.org/10.1007/978-3-642-32147-4_40
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