{"type":"ScholarlyArticle","title":"Non-Binary Constraints and Optimal Dual-Graph Representations","authors":[{"name":"Gianluigi Greco","slug":"gianluigi-greco","given":"Gianluigi","family":"Greco","affiliation":""},{"name":"Francesco Scarcello","slug":"francesco-scarcello","given":"Francesco","family":"Scarcello","affiliation":""}],"abstract":"We study the relationships among structural methods for identifying and solving tractable classes of Constraint Satisfaction Problems (CSPs). In particular, we first answer a long-standing question about the notion of biconnected components applied to an \"optimal\" reduct of the dual constraint-graph, by showing that this notion is in fact equivalent to the hinge decomposition method. Then, we give a precise characterization of the relationship between the treewidth notion applied to the hidden-variable encoding of a CSP and the same notion applied to some optimal reduct of the dual constraint-graph. Finally, we face the open problem of computing such an optimal reduct. We provide an algorithm that outputs an approximation of an optimal tree decomposition, and give a qualitative explanation of the difference between this graph-based method and more general hypergraph-based methods.","doi":null,"url":"https://ijcai.org/proceedings/2003/33","pdf":"https://ijcai.org/proceedings/2003/0033.pdf","markdown":"https://ijcai.org/proceedings/2003/33.md","bibtex":"https://ijcai.org/proceedings/2003/bibtex/33","volume":{"slug":"2003","title":"Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2003","url":"https://ijcai.org/proceedings/2003/","year":2003,"location":"Acapulco, Mexico","dates":"","editors":"Georg Gottlob","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":33,"pages":{"first":227,"last":231},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}