--- _id: '3117' abstract: - lang: eng 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. author: - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov citation: ama: Kolmogorov V. Minimizing a sum of submodular functions. Discrete Applied Mathematics. 2012;160(15):2246-2258. doi:10.1016/j.dam.2012.05.025 apa: Kolmogorov, V. (2012). Minimizing a sum of submodular functions. Discrete Applied Mathematics. Elsevier. https://doi.org/10.1016/j.dam.2012.05.025 chicago: Kolmogorov, Vladimir. “Minimizing a Sum of Submodular Functions.” Discrete Applied Mathematics. Elsevier, 2012. https://doi.org/10.1016/j.dam.2012.05.025. ieee: V. Kolmogorov, “Minimizing a sum of submodular functions,” Discrete Applied Mathematics, vol. 160, no. 15. Elsevier, pp. 2246–2258, 2012. ista: Kolmogorov V. 2012. Minimizing a sum of submodular functions. Discrete Applied Mathematics. 160(15), 2246–2258. mla: Kolmogorov, Vladimir. “Minimizing a Sum of Submodular Functions.” Discrete Applied Mathematics, vol. 160, no. 15, Elsevier, 2012, pp. 2246–58, doi:10.1016/j.dam.2012.05.025. short: V. Kolmogorov, Discrete Applied Mathematics 160 (2012) 2246–2258. date_created: 2018-12-11T12:01:29Z date_published: 2012-10-01T00:00:00Z date_updated: 2021-01-12T07:41:11Z day: '01' department: - _id: VlKo doi: 10.1016/j.dam.2012.05.025 intvolume: ' 160' issue: '15' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1006.1990 month: '10' oa: 1 oa_version: Preprint page: 2246 - 2258 publication: Discrete Applied Mathematics publication_status: published publisher: Elsevier publist_id: '3582' quality_controlled: '1' scopus_import: 1 status: public title: Minimizing a sum of submodular functions type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 160 year: '2012' ...