{"scopus_import":"1","ddc":["000"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2019-07-29T12:23:29Z","file":[{"relation":"main_file","file_size":575475,"date_created":"2019-07-31T07:01:45Z","content_type":"application/pdf","access_level":"open_access","file_id":"6738","creator":"dernst","date_updated":"2020-07-14T12:47:38Z","file_name":"2019_LIPICS_Kolmogorov.pdf","checksum":"f5ebee8eec6ae09e30365578ee63a492"}],"oa_version":"Published Version","oa":1,"volume":132,"conference":{"end_date":"2019-07-12","start_date":"2019-07-08","location":"Patras, Greece","name":"ICALP: Automata, Languages and Programming"},"doi":"10.4230/LIPICS.ICALP.2019.77","date_updated":"2025-04-14T13:42:17Z","file_date_updated":"2020-07-14T12:47:38Z","page":"77:1-77:12","date_published":"2019-07-01T00:00:00Z","arxiv":1,"ec_funded":1,"day":"01","year":"2019","month":"07","external_id":{"arxiv":["1803.02289"]},"status":"public","project":[{"grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice","call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425"}],"language":[{"iso":"eng"}],"license":"https://creativecommons.org/licenses/by/4.0/","alternative_title":["LIPIcs"],"quality_controlled":"1","type":"conference","has_accepted_license":"1","publication_status":"published","title":"Testing the complexity of a valued CSP language","intvolume":"       132","department":[{"_id":"VlKo"}],"_id":"6725","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","publication_identifier":{"isbn":["978-3-95977-109-2"],"issn":["1868-8969"]},"author":[{"full_name":"Kolmogorov, Vladimir","last_name":"Kolmogorov","first_name":"Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87"}],"publication":"46th International Colloquium on Automata, Languages and Programming","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"abstract":[{"lang":"eng","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."}],"article_processing_charge":"No"}