{"type":"ScholarlyArticle","title":"Semantic Width and the Fixed-Parameter Tractability of Constraint Satisfaction Problems","authors":[{"name":"Hubie Chen","slug":"hubie-chen","given":"Hubie","family":"Chen","affiliation":"Birkbeck , University of London"},{"name":"Georg Gottlob","slug":"georg-gottlob","given":"Georg","family":"Gottlob","affiliation":"Oxford University; TU Wien"},{"name":"Matthias Lanzinger","slug":"matthias-lanzinger","given":"Matthias","family":"Lanzinger","affiliation":"TU Wien"},{"name":"Reinhard Pichler","slug":"reinhard-pichler","given":"Reinhard","family":"Pichler","affiliation":"TU Wien"}],"abstract":"Constraint satisfaction problems (CSPs) are an important formal framework for the uniform treatment of various prominent AI tasks, e.g., coloring or scheduling problems. Solving CSPs is, in general, known to be NP-complete and fixed-parameter intractable when parameterized by their constraint scopes.  We give a characterization of those classes of CSPs for which the problem becomes fixed-parameter tractable. Our characterization significantly increases the utility of the CSP framework by making it possible to decide the fixed-parameter tractability of problems via their CSP formulations. We further extend our characterization to the evaluation of unions of conjunctive queries, a fundamental problem in databases. Furthermore, we provide some new insight on the frontier of PTIME solvability of CSPs. In particular, we observe that bounded fractional hypertree width is more general than bounded hypertree width only for classes that exhibit a certain type of exponential growth. The presented work resolves a long-standing open problem and yields powerful new tools for complexity research in AI and database theory.","doi":"10.24963/ijcai.2020/239","url":"https://ijcai.org/proceedings/2020/239","pdf":"https://ijcai.org/proceedings/2020/0239.pdf","markdown":"https://ijcai.org/proceedings/2020/239.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/239","volume":{"slug":"2020","title":"Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2020","url":"https://ijcai.org/proceedings/2020/","year":2020,"location":"Yokohama","dates":"January 2021 (postponed from 11-17 July 2020)","editors":"Christian Bessiere","isbn":"978-0-9992411-6-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2020"},"section":"Knowledge Representation and Reasoning","track":"Main track","number":239,"pages":{"first":1726,"last":1733},"keywords":["Multidisciplinary Topics and Applications: Databases","Constraints and SAT: Constraint Satisfaction","Knowledge Representation and Reasoning: Computational Complexity of Reasoning"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/24375/file_24375.m3u8","length_sec":293,"provider":"hls"}],"references":[{"position":1,"raw":"[Adler et al., 2007] Isolde Adler, Georg Gottlob, and Martin Grohe. 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