{"type":"ScholarlyArticle","title":"Decision Diagrams for the Computation of Semiring Valuations","authors":[{"name":"Nic Wilson","slug":"nic-wilson","given":"Nic","family":"Wilson","affiliation":"Cork Constraint Computation Centre; Department of Computer Science , University College Cork , Ireland"}],"abstract":"This paper describes a new approach to computation in a semiring-based system, which includes semiring-based CSPs (in particular weighted CSPs, fuzzy CSPs and standard CSPs) as well as Bayesian networks. The approach to computation is based on what we call semiring-labelled decision diagrams (SLDDs). These can be generated in a similar way to a standard search tree (decision tree) for solving a CSP, but some nodes are merged, creating a more compact representation; for certain classes of CSPs, the number of nodes in the resulting network will be a tiny fraction of the number of nodes in the corresponding search tree. A method is given for generating an SLDD that represents e.g., a particular instance of a semiring-based CSP; it is shown how this can be used to perform various computations of interest, such as solving a semiring-based CSP, finding optimal solutions, determining the possible values of each variable and counting solutions of a CSP.","doi":null,"url":"https://ijcai.org/proceedings/2005/93","pdf":"https://ijcai.org/proceedings/2005/0093.pdf","markdown":"https://ijcai.org/proceedings/2005/93.md","bibtex":"https://ijcai.org/proceedings/2005/bibtex/93","volume":{"slug":"2005","title":"Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2005","url":"https://ijcai.org/proceedings/2005/","year":2005,"location":"Edinburgh, Scotland, UK","dates":"","editors":"","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":93,"pages":{"first":331,"last":335},"keywords":[],"videos":[],"references":[{"position":1,"raw":"[Amilhastre et al., 2002] J. 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