@inproceedings{2930, abstract = {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. }, author = {Huber, Anna and Kolmogorov, Vladimir}, location = {Athens, Greece}, pages = {451 -- 462}, publisher = {Springer}, title = {{Towards minimizing k-submodular functions}}, doi = {10.1007/978-3-642-32147-4_40}, volume = {7422}, year = {2012}, }