{"date_updated":"2021-01-12T07:41:11Z","month":"10","author":[{"id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","full_name":"Kolmogorov, Vladimir","first_name":"Vladimir","last_name":"Kolmogorov"}],"publication":"Discrete Applied Mathematics","day":"01","doi":"10.1016/j.dam.2012.05.025","page":"2246 - 2258","type":"journal_article","abstract":[{"text":"We consider the problem of minimizing a function represented as a sum of submodular terms. We assume each term allows an efficient computation of exchange capacities. This holds, for example, for terms depending on a small number of variables, or for certain cardinality-dependent terms. A naive application of submodular minimization algorithms would not exploit the existence of specialized exchange capacity subroutines for individual terms. To overcome this, we cast the problem as a submodular flow (SF) problem in an auxiliary graph in such a way that applying most existing SF algorithms would rely only on these subroutines. We then explore in more detail Iwata's capacity scaling approach for submodular flows (Iwata 1997 [19]). In particular, we show how to improve its complexity in the case when the function contains cardinality-dependent terms.","lang":"eng"}],"main_file_link":[{"url":"http://arxiv.org/abs/1006.1990","open_access":"1"}],"_id":"3117","language":[{"iso":"eng"}],"department":[{"_id":"VlKo"}],"issue":"15","citation":{"ama":"Kolmogorov V. Minimizing a sum of submodular functions. <i>Discrete Applied Mathematics</i>. 2012;160(15):2246-2258. doi:<a href=\"https://doi.org/10.1016/j.dam.2012.05.025\">10.1016/j.dam.2012.05.025</a>","ista":"Kolmogorov V. 2012. Minimizing a sum of submodular functions. Discrete Applied Mathematics. 160(15), 2246–2258.","chicago":"Kolmogorov, Vladimir. “Minimizing a Sum of Submodular Functions.” <i>Discrete Applied Mathematics</i>. Elsevier, 2012. <a href=\"https://doi.org/10.1016/j.dam.2012.05.025\">https://doi.org/10.1016/j.dam.2012.05.025</a>.","apa":"Kolmogorov, V. (2012). Minimizing a sum of submodular functions. <i>Discrete Applied Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.dam.2012.05.025\">https://doi.org/10.1016/j.dam.2012.05.025</a>","short":"V. Kolmogorov, Discrete Applied Mathematics 160 (2012) 2246–2258.","mla":"Kolmogorov, Vladimir. “Minimizing a Sum of Submodular Functions.” <i>Discrete Applied Mathematics</i>, vol. 160, no. 15, Elsevier, 2012, pp. 2246–58, doi:<a href=\"https://doi.org/10.1016/j.dam.2012.05.025\">10.1016/j.dam.2012.05.025</a>.","ieee":"V. Kolmogorov, “Minimizing a sum of submodular functions,” <i>Discrete Applied Mathematics</i>, vol. 160, no. 15. Elsevier, pp. 2246–2258, 2012."},"date_published":"2012-10-01T00:00:00Z","publication_status":"published","scopus_import":1,"year":"2012","publisher":"Elsevier","publist_id":"3582","date_created":"2018-12-11T12:01:29Z","volume":160,"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","intvolume":"       160","oa":1,"status":"public","title":"Minimizing a sum of submodular functions","quality_controlled":"1"}