{"month":"07","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. An instance of the problem is specified by a sum of cost functions from the language with the goal to minimise the sum. We study which classes of finite-valued languages can be solved exactly by the basic linear programming relaxation (BLP). Thapper and Živný showed [20] that if BLP solves the language then the language admits a binary commutative fractional polymorphism. We prove that the converse is also true. This leads to a necessary and a sufficient condition which can be checked in polynomial time for a given language. In contrast, the previous necessary and sufficient condition due to [20] involved infinitely many inequalities. More recently, Thapper and Živný [21] showed (using, in particular, a technique introduced in this paper) that core languages that do not satisfy our condition are NP-hard. Taken together, these results imply that a finite-valued language can either be solved using Linear Programming or is NP-hard."}],"language":[{"iso":"eng"}],"scopus_import":1,"citation":{"mla":"Kolmogorov, Vladimir. <i>The Power of Linear Programming for Finite-Valued CSPs: A Constructive Characterization</i>. Vol. 7965, no. 1, Springer, 2013, pp. 625–36, doi:<a href=\"https://doi.org/10.1007/978-3-642-39206-1_53\">10.1007/978-3-642-39206-1_53</a>.","apa":"Kolmogorov, V. (2013). The power of linear programming for finite-valued CSPs: A constructive characterization (Vol. 7965, pp. 625–636). Presented at the ICALP: Automata, Languages and Programming, Riga, Latvia: Springer. <a href=\"https://doi.org/10.1007/978-3-642-39206-1_53\">https://doi.org/10.1007/978-3-642-39206-1_53</a>","ieee":"V. Kolmogorov, “The power of linear programming for finite-valued CSPs: A constructive characterization,” presented at the ICALP: Automata, Languages and Programming, Riga, Latvia, 2013, vol. 7965, no. 1, pp. 625–636.","ista":"Kolmogorov V. 2013. The power of linear programming for finite-valued CSPs: A constructive characterization. ICALP: Automata, Languages and Programming, LNCS, vol. 7965, 625–636.","ama":"Kolmogorov V. The power of linear programming for finite-valued CSPs: A constructive characterization. In: Vol 7965. Springer; 2013:625-636. doi:<a href=\"https://doi.org/10.1007/978-3-642-39206-1_53\">10.1007/978-3-642-39206-1_53</a>","short":"V. Kolmogorov, in:, Springer, 2013, pp. 625–636.","chicago":"Kolmogorov, Vladimir. “The Power of Linear Programming for Finite-Valued CSPs: A Constructive Characterization,” 7965:625–36. Springer, 2013. <a href=\"https://doi.org/10.1007/978-3-642-39206-1_53\">https://doi.org/10.1007/978-3-642-39206-1_53</a>."},"day":"01","date_updated":"2023-02-23T10:35:42Z","publist_id":"4383","issue":"1","external_id":{"arxiv":["1207.7213"]},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publication_status":"published","date_published":"2013-07-01T00:00:00Z","year":"2013","oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1207.7213"}],"_id":"2518","related_material":{"record":[{"status":"public","relation":"later_version","id":"2271"}]},"status":"public","department":[{"_id":"VlKo"}],"publisher":"Springer","intvolume":"      7965","alternative_title":["LNCS"],"author":[{"last_name":"Kolmogorov","first_name":"Vladimir","full_name":"Kolmogorov, Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87"}],"doi":"10.1007/978-3-642-39206-1_53","type":"conference","title":"The power of linear programming for finite-valued CSPs: A constructive characterization","date_created":"2018-12-11T11:58:08Z","oa_version":"Preprint","page":"625 - 636","quality_controlled":"1","volume":7965,"conference":{"start_date":"2013-07-08","location":"Riga, Latvia","name":"ICALP: Automata, Languages and Programming","end_date":"2013-07-12"}}