{"quality_controlled":"1","publication_status":"published","_id":"2271","issue":"1","related_material":{"record":[{"id":"2518","relation":"earlier_version","status":"public"}]},"status":"public","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1311.4219"}],"month":"02","author":[{"last_name":"Kolmogorov","first_name":"Vladimir","full_name":"Kolmogorov, Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Thapper, Johan","first_name":"Johan","last_name":"Thapper"},{"full_name":"Živný, Stanislav","first_name":"Stanislav","last_name":"Živný"}],"publisher":"SIAM","doi":"10.1137/130945648","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","page":"1 - 36","isi":1,"year":"2015","title":"The power of linear programming for general-valued CSPs","external_id":{"arxiv":["1311.4219"],"isi":["000353967100001"]},"publication":"SIAM Journal on Computing","day":"01","intvolume":"        44","language":[{"iso":"eng"}],"volume":44,"department":[{"_id":"VlKo"}],"date_published":"2015-02-01T00:00:00Z","scopus_import":"1","oa_version":"Preprint","article_processing_charge":"No","date_updated":"2025-09-23T14:14:57Z","oa":1,"arxiv":1,"publist_id":"4673","citation":{"ama":"Kolmogorov V, Thapper J, Živný S. The power of linear programming for general-valued CSPs. <i>SIAM Journal on Computing</i>. 2015;44(1):1-36. doi:<a href=\"https://doi.org/10.1137/130945648\">10.1137/130945648</a>","ista":"Kolmogorov V, Thapper J, Živný S. 2015. The power of linear programming for general-valued CSPs. SIAM Journal on Computing. 44(1), 1–36.","short":"V. Kolmogorov, J. Thapper, S. Živný, SIAM Journal on Computing 44 (2015) 1–36.","apa":"Kolmogorov, V., Thapper, J., &#38; Živný, S. (2015). The power of linear programming for general-valued CSPs. <i>SIAM Journal on Computing</i>. SIAM. <a href=\"https://doi.org/10.1137/130945648\">https://doi.org/10.1137/130945648</a>","chicago":"Kolmogorov, Vladimir, Johan Thapper, and Stanislav Živný. “The Power of Linear Programming for General-Valued CSPs.” <i>SIAM Journal on Computing</i>. SIAM, 2015. <a href=\"https://doi.org/10.1137/130945648\">https://doi.org/10.1137/130945648</a>.","mla":"Kolmogorov, Vladimir, et al. “The Power of Linear Programming for General-Valued CSPs.” <i>SIAM Journal on Computing</i>, vol. 44, no. 1, SIAM, 2015, pp. 1–36, doi:<a href=\"https://doi.org/10.1137/130945648\">10.1137/130945648</a>.","ieee":"V. Kolmogorov, J. Thapper, and S. Živný, “The power of linear programming for general-valued CSPs,” <i>SIAM Journal on Computing</i>, vol. 44, no. 1. SIAM, pp. 1–36, 2015."},"type":"journal_article","date_created":"2018-12-11T11:56:41Z","abstract":[{"lang":"eng","text":"A class of valued constraint satisfaction problems (VCSPs) is characterised by a valued constraint language, a fixed set of cost functions on a finite domain. Finite-valued constraint languages contain functions that take on rational costs and general-valued constraint languages contain functions that take on rational or infinite costs. An instance of the problem is specified by a sum of functions from the language with the goal to minimise the sum. This framework includes and generalises well-studied constraint satisfaction problems (CSPs) and maximum constraint satisfaction problems (Max-CSPs).\r\nOur main result is a precise algebraic characterisation of valued constraint languages whose instances can be solved exactly by the basic linear programming relaxation (BLP). For a general-valued constraint language Γ, BLP is a decision procedure for Γ if and only if Γ admits a symmetric fractional polymorphism of every arity. For a finite-valued constraint language Γ, BLP is a decision procedure if and only if Γ admits a symmetric fractional polymorphism of some arity, or equivalently, if Γ admits a symmetric fractional polymorphism of arity 2.\r\nUsing these results, we obtain tractability of several novel and previously widely-open classes of VCSPs, including problems over valued constraint languages that are: (1) submodular on arbitrary lattices; (2) bisubmodular (also known as k-submodular) on arbitrary finite domains; (3) weakly (and hence strongly) tree-submodular on arbitrary trees. "}]}