{"month":"04","arxiv":1,"language":[{"iso":"eng"}],"year":"2012","oa":1,"doi":"10.1007/978-3-642-32147-4_40","conference":{"name":"ISCO: International Symposium on Combinatorial Optimization","location":"Athens, Greece","end_date":"2012-04-21","start_date":"2012-04-19"},"page":"451 - 462","volume":7422,"status":"public","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","type":"conference","external_id":{"arxiv":["1309.5469"]},"date_created":"2018-12-11T12:00:24Z","title":"Towards minimizing k-submodular functions","author":[{"last_name":"Huber","first_name":"Anna","full_name":"Huber, Anna"},{"first_name":"Vladimir","last_name":"Kolmogorov","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","full_name":"Kolmogorov, Vladimir"}],"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"}],"date_updated":"2025-06-11T08:08:15Z","main_file_link":[{"url":"http://arxiv.org/abs/1309.5469","open_access":"1"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","date_published":"2012-04-01T00:00:00Z","quality_controlled":"1","citation":{"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.","short":"A. Huber, V. Kolmogorov, in:, Springer, 2012, pp. 451–462.","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>.","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>.","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>","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>"},"publisher":"Springer","publist_id":"3806","intvolume":"      7422","alternative_title":["LNCS"],"department":[{"_id":"VlKo"}],"scopus_import":"1","_id":"2930","oa_version":"Preprint","article_processing_charge":"No","day":"01"}