{"type":"conference","alternative_title":["LNCS"],"related_material":{"record":[{"status":"public","id":"2271","relation":"later_version"}]},"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."}],"publication_status":"published","oa":1,"date_updated":"2021-01-12T07:23:03Z","department":[{"_id":"VlKo"}],"intvolume":" 7965","page":"625 - 636","month":"07","doi":"10.1007/978-3-642-39206-1_53","year":"2013","main_file_link":[{"url":"http://arxiv.org/abs/1207.7213","open_access":"1"}],"publist_id":"4383","external_id":{"arxiv":["1207.7213"]},"quality_controlled":"1","volume":7965,"scopus_import":1,"author":[{"last_name":"Kolmogorov","full_name":"Kolmogorov, Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","first_name":"Vladimir"}],"status":"public","day":"01","title":"The power of linear programming for finite-valued CSPs: A constructive characterization","publisher":"Springer","date_published":"2013-07-01T00:00:00Z","oa_version":"Preprint","citation":{"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.","short":"V. Kolmogorov, in:, Springer, 2013, pp. 625–636.","mla":"Kolmogorov, Vladimir. The Power of Linear Programming for Finite-Valued CSPs: A Constructive Characterization. Vol. 7965, no. 1, Springer, 2013, pp. 625–36, doi:10.1007/978-3-642-39206-1_53.","ama":"Kolmogorov V. The power of linear programming for finite-valued CSPs: A constructive characterization. In: Vol 7965. Springer; 2013:625-636. doi:10.1007/978-3-642-39206-1_53","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. https://doi.org/10.1007/978-3-642-39206-1_53","chicago":"Kolmogorov, Vladimir. “The Power of Linear Programming for Finite-Valued CSPs: A Constructive Characterization,” 7965:625–36. Springer, 2013. https://doi.org/10.1007/978-3-642-39206-1_53.","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."},"conference":{"start_date":"2013-07-08","end_date":"2013-07-12","location":"Riga, Latvia","name":"ICALP: Automata, Languages and Programming"},"issue":"1","language":[{"iso":"eng"}],"date_created":"2018-12-11T11:58:08Z","_id":"2518","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87"}