[{"oa_version":"Preprint","intvolume":" 7422","status":"public","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"2930","abstract":[{"lang":"eng"}],"alternative_title":[],"type":"conference","date_published":"2012-04-01T00:00:00Z","page":"451 - 462","citation":{"chicago":"Huber, Anna, and Vladimir Kolmogorov. “Towards Minimizing K-Submodular Functions,” 7422:451–62. Springer, 2012. https://doi.org/10.1007/978-3-642-32147-4_40.","mla":"Huber, Anna, and Vladimir Kolmogorov. Towards Minimizing K-Submodular Functions. Vol. 7422, Springer, 2012, pp. 451–62, doi:10.1007/978-3-642-32147-4_40.","short":"A. Huber, V. Kolmogorov, in:, Springer, 2012, pp. 451–462.","ista":"Huber A, Kolmogorov V. 2012. Towards minimizing k-submodular functions. ISCO: International Symposium on Combinatorial Optimization, LNCS, vol. 7422, 451–462.","apa":"Huber, A., & 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. https://doi.org/10.1007/978-3-642-32147-4_40","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."},"uri_base":"https://research-explorer.ista.ac.at","day":"01","scopus_import":1,"dc":{"creator":["Huber, Anna","Kolmogorov, Vladimir"],"type":["info:eu-repo/semantics/conferenceObject","doc-type:conferenceObject","text","http://purl.org/coar/resource_type/c_5794"],"identifier":["https://research-explorer.ista.ac.at/record/2930"],"description":["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":["2012"],"language":["eng"],"rights":["info:eu-repo/semantics/openAccess"],"source":["Huber A, Kolmogorov V. Towards minimizing k-submodular functions. In: Vol 7422. Springer; 2012:451-462. doi:10.1007/978-3-642-32147-4_40"],"relation":["info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-642-32147-4_40"],"publisher":["Springer"],"title":["Towards minimizing k-submodular functions","LNCS"]},"volume":7422,"dini_type":"doc-type:conferenceObject","date_created":"2018-12-11T12:00:24Z","date_updated":"2021-01-12T07:00:46Z","author":[{"last_name":"Huber","first_name":"Anna"},{"id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","last_name":"Kolmogorov","first_name":"Vladimir"}],"department":[{"tree":[{"_id":"ResearchGroups"},{"_id":"IST"}],"_id":"VlKo"}],"publication_status":"published","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","creator":{"id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","login":"kschuh"},"publist_id":"3806","language":[{}],"conference":{"name":"ISCO: International Symposium on Combinatorial Optimization","end_date":"2012-04-21","start_date":"2012-04-19","location":"Athens, Greece"},"quality_controlled":"1","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1309.5469"}],"oa":1,"month":"04"}]