{"author":[{"first_name":"Anna","full_name":"Huber, Anna","last_name":"Huber"},{"last_name":"Kolmogorov","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","full_name":"Kolmogorov, Vladimir","first_name":"Vladimir"}],"conference":{"name":"ISCO: International Symposium on Combinatorial Optimization","start_date":"2012-04-19","location":"Athens, Greece","end_date":"2012-04-21"},"date_created":"2018-12-11T12:00:24Z","abstract":[{"lang":"eng","text":"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.\r\n\r\nIn 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.\r\n"}],"doi":"10.1007/978-3-642-32147-4_40","title":"Towards minimizing k-submodular functions","publication_status":"published","oa":1,"acknowledgement":"We would like to thank Andrei Krokhin for encourag- ing our cooperation, for helpful discussions, and for his critical reading of the manuscript.\r\n","date_updated":"2021-01-12T07:00:46Z","date_published":"2012-04-01T00:00:00Z","quality_controlled":"1","citation":{"ista":"Huber A, Kolmogorov V. 2012. Towards minimizing k-submodular functions. ISCO: International Symposium on Combinatorial Optimization, LNCS, vol. 7422, 451–462.","chicago":"Huber, Anna, and Vladimir Kolmogorov. “Towards Minimizing K-Submodular Functions,” 7422:451–62. Springer, 2012. <a href=\"https://doi.org/10.1007/978-3-642-32147-4_40\">https://doi.org/10.1007/978-3-642-32147-4_40</a>.","mla":"Huber, Anna, and Vladimir Kolmogorov. <i>Towards Minimizing K-Submodular Functions</i>. Vol. 7422, Springer, 2012, pp. 451–62, doi:<a href=\"https://doi.org/10.1007/978-3-642-32147-4_40\">10.1007/978-3-642-32147-4_40</a>.","ieee":"A. Huber and V. Kolmogorov, “Towards minimizing k-submodular functions,” presented at the ISCO: International Symposium on Combinatorial Optimization, Athens, Greece, 2012, vol. 7422, pp. 451–462.","apa":"Huber, A., &#38; Kolmogorov, V. (2012). Towards minimizing k-submodular functions (Vol. 7422, pp. 451–462). Presented at the ISCO: International Symposium on Combinatorial Optimization, Athens, Greece: Springer. <a href=\"https://doi.org/10.1007/978-3-642-32147-4_40\">https://doi.org/10.1007/978-3-642-32147-4_40</a>","short":"A. Huber, V. Kolmogorov, in:, Springer, 2012, pp. 451–462.","ama":"Huber A, Kolmogorov V. Towards minimizing k-submodular functions. In: Vol 7422. Springer; 2012:451-462. doi:<a href=\"https://doi.org/10.1007/978-3-642-32147-4_40\">10.1007/978-3-642-32147-4_40</a>"},"scopus_import":1,"year":"2012","status":"public","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publist_id":"3806","oa_version":"Preprint","month":"04","volume":7422,"intvolume":"      7422","page":"451 - 462","day":"01","main_file_link":[{"url":"http://arxiv.org/abs/1309.5469","open_access":"1"}],"publisher":"Springer","language":[{"iso":"eng"}],"alternative_title":["LNCS"],"type":"conference","department":[{"_id":"VlKo"}],"_id":"2930"}