{"project":[{"_id":"25FBA906-B435-11E9-9278-68D0E5697425","name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160","call_identifier":"FP7"}],"type":"conference","language":[{"iso":"eng"}],"volume":132,"publication_status":"published","file_date_updated":"2020-07-14T12:47:38Z","oa_version":"Published Version","scopus_import":"1","external_id":{"arxiv":["1803.02289"]},"date_created":"2019-07-29T12:23:29Z","department":[{"_id":"VlKo"}],"publication":"46th International Colloquium on Automata, Languages and Programming","date_updated":"2025-07-10T11:53:47Z","page":"77:1-77:12","publication_identifier":{"issn":["1868-8969"],"isbn":["978-3-95977-109-2"]},"doi":"10.4230/LIPICS.ICALP.2019.77","status":"public","alternative_title":["LIPIcs"],"month":"07","intvolume":"       132","has_accepted_license":"1","abstract":[{"text":"A Valued Constraint Satisfaction Problem (VCSP) provides a common framework that can express a wide range of discrete optimization problems. A VCSP instance is given by a finite set of variables, a finite domain of labels, and an objective function to be minimized. This function is represented as a sum of terms where each term depends on a subset of the variables. To obtain different classes of optimization problems, one can restrict all terms to come from a fixed set Γ of cost functions, called a language. \r\nRecent breakthrough results have established a complete complexity classification of such classes with respect to language Γ: if all cost functions in Γ satisfy a certain algebraic condition then all Γ-instances can be solved in polynomial time, otherwise the problem is NP-hard. Unfortunately, testing this condition for a given language Γ is known to be NP-hard. We thus study exponential algorithms for this meta-problem. We show that the tractability condition of a finite-valued language Γ can be tested in O(3‾√3|D|⋅poly(size(Γ))) time, where D is the domain of Γ and poly(⋅) is some fixed polynomial. We also obtain a matching lower bound under the Strong Exponential Time Hypothesis (SETH). More precisely, we prove that for any constant δ<1 there is no O(3‾√3δ|D|) algorithm, assuming that SETH holds.","lang":"eng"}],"arxiv":1,"oa":1,"quality_controlled":"1","citation":{"chicago":"Kolmogorov, Vladimir. “Testing the Complexity of a Valued CSP Language.” In <i>46th International Colloquium on Automata, Languages and Programming</i>, 132:77:1-77:12. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. <a href=\"https://doi.org/10.4230/LIPICS.ICALP.2019.77\">https://doi.org/10.4230/LIPICS.ICALP.2019.77</a>.","mla":"Kolmogorov, Vladimir. “Testing the Complexity of a Valued CSP Language.” <i>46th International Colloquium on Automata, Languages and Programming</i>, vol. 132, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 77:1-77:12, doi:<a href=\"https://doi.org/10.4230/LIPICS.ICALP.2019.77\">10.4230/LIPICS.ICALP.2019.77</a>.","ista":"Kolmogorov V. 2019. Testing the complexity of a valued CSP language. 46th International Colloquium on Automata, Languages and Programming. ICALP: Automata, Languages and Programming, LIPIcs, vol. 132, 77:1-77:12.","ama":"Kolmogorov V. Testing the complexity of a valued CSP language. In: <i>46th International Colloquium on Automata, Languages and Programming</i>. Vol 132. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019:77:1-77:12. doi:<a href=\"https://doi.org/10.4230/LIPICS.ICALP.2019.77\">10.4230/LIPICS.ICALP.2019.77</a>","apa":"Kolmogorov, V. (2019). Testing the complexity of a valued CSP language. In <i>46th International Colloquium on Automata, Languages and Programming</i> (Vol. 132, p. 77:1-77:12). Patras, Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPICS.ICALP.2019.77\">https://doi.org/10.4230/LIPICS.ICALP.2019.77</a>","ieee":"V. Kolmogorov, “Testing the complexity of a valued CSP language,” in <i>46th International Colloquium on Automata, Languages and Programming</i>, Patras, Greece, 2019, vol. 132, p. 77:1-77:12.","short":"V. Kolmogorov, in:, 46th International Colloquium on Automata, Languages and Programming, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 77:1-77:12."},"ddc":["000"],"year":"2019","day":"01","date_published":"2019-07-01T00:00:00Z","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","article_processing_charge":"No","file":[{"date_created":"2019-07-31T07:01:45Z","file_size":575475,"creator":"dernst","file_id":"6738","date_updated":"2020-07-14T12:47:38Z","content_type":"application/pdf","checksum":"f5ebee8eec6ae09e30365578ee63a492","file_name":"2019_LIPICS_Kolmogorov.pdf","relation":"main_file","access_level":"open_access"}],"_id":"6725","conference":{"start_date":"2019-07-08","name":"ICALP: Automata, Languages and Programming","end_date":"2019-07-12","location":"Patras, Greece"},"ec_funded":1,"author":[{"id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","first_name":"Vladimir","full_name":"Kolmogorov, Vladimir","last_name":"Kolmogorov"}],"title":"Testing the complexity of a valued CSP language","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"}