{"department":[{"_id":"VlKo"}],"external_id":{"arxiv":["1207.7213"]},"doi":"10.1007/978-3-642-39206-1_53","title":"The power of linear programming for finite-valued CSPs: A constructive characterization","conference":{"end_date":"2013-07-12","location":"Riga, Latvia","start_date":"2013-07-08","name":"ICALP: Automata, Languages and Programming"},"oa":1,"abstract":[{"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.","lang":"eng"}],"date_created":"2018-12-11T11:58:08Z","author":[{"last_name":"Kolmogorov","full_name":"Kolmogorov, Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","first_name":"Vladimir"}],"intvolume":"      7965","publisher":"Springer","year":"2013","volume":7965,"date_published":"2013-07-01T00:00:00Z","citation":{"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>","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>.","short":"V. Kolmogorov, in:, Springer, 2013, pp. 625–636.","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.","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>.","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>","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."},"type":"conference","related_material":{"record":[{"status":"public","id":"2271","relation":"later_version"}]},"oa_version":"Preprint","status":"public","issue":"1","scopus_import":1,"language":[{"iso":"eng"}],"page":"625 - 636","alternative_title":["LNCS"],"_id":"2518","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","day":"01","month":"07","main_file_link":[{"url":"http://arxiv.org/abs/1207.7213","open_access":"1"}],"publist_id":"4383","publication_status":"published","date_updated":"2023-02-23T10:35:42Z"}