{"type":"ScholarlyArticle","title":"Threshold Treewidth and Hypertree Width","authors":[{"name":"Robert Ganian","slug":"robert-ganian","given":"Robert","family":"Ganian","affiliation":"TU Wien , Vienna , Austria"},{"name":"Andre Schidler","slug":"andre-schidler","given":"Andre","family":"Schidler","affiliation":"TU Wien , Vienna , Austria"},{"name":"Manuel Sorge","slug":"manuel-sorge","given":"Manuel","family":"Sorge","affiliation":"University of Warsaw , Warsaw , Poland"},{"name":"Stefan Szeider","slug":"stefan-szeider","given":"Stefan","family":"Szeider","affiliation":"TU Wien , Vienna , Austria"}],"abstract":"Treewidth and hypertree width have proven to be highly successful structural parameters in the context of the Constraint Satisfaction Problem (CSP). When either of these parameters is bounded by a constant, then CSP becomes solvable in polynomial time. However, here the order of the polynomial in the running time depends on the width, and this is known to be unavoidable; therefore, the problem is not fixed-parameter tractable parameterized by either of these width measures. Here we introduce an enhancement of tree and hypertree width through a novel notion of thresholds, allowing the associated decompositions to take into account information about the computational costs associated with solving the given CSP instance. Aside from introducing these notions, we obtain efficient theoretical as well as empirical algorithms for computing threshold treewidth and hypertree width and show that these parameters give rise to fixed-parameter algorithms for CSP as well as other, more general problems. We complement our theoretical results with experimental evaluations in terms of heuristics as well as exact methods based on SAT/SMT encodings.","doi":"10.24963/ijcai.2020/263","url":"https://ijcai.org/proceedings/2020/263","pdf":"https://ijcai.org/proceedings/2020/0263.pdf","markdown":"https://ijcai.org/proceedings/2020/263.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/263","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":263,"pages":{"first":1898,"last":1904},"keywords":["Constraints and SAT: Constraint Satisfaction","Constraints and SAT: Satisfiability Modulo Theories","Knowledge Representation and Reasoning: Computational Complexity of Reasoning"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/25047/file_25047.m3u8","length_sec":279,"provider":"hls"}],"references":[{"position":1,"raw":"[Abseher et al., 2017] Michael Abseher, Nysret Musliu, and Stefan Woltran. 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