{"type":"ScholarlyArticle","title":"Consistency Checking of Basic Cardinal Constraints over Connected Regions","authors":[{"name":"Isabel Navarrete","slug":"isabel-navarrete","given":"Isabel","family":"Navarrete","affiliation":""},{"name":"Antonio Morales","slug":"antonio-morales","given":"Antonio","family":"Morales","affiliation":""},{"name":"Guido Sciavicco","slug":"guido-sciavicco","given":"Guido","family":"Sciavicco","affiliation":""}],"abstract":"In this paper we study a recent formal model for qualitative spatial reasoning with cardinal direction relations. We give an O(n^4) algorithm to check the consistency of a network of basic cardinal constraints with variables ranging over the set of connected regions homeomorphic to the closed unit disk (which includes a wide variety of irregular-shaped regions). To the best of our knowledge, this was an open problem. A previous algorithm for a domain that includes also disconnected regions works in $O(n^5)$, but, for the problem we consider here, such an algorithm cannot be used. Using the new algorithm we also show that the problem of deciding the consistency of a network of disjunctive cardinal constraints with variables ranging over the set of connected regions is $NP$-Complete. Our main contribution is based on results from the field of combinatorial geometry.","doi":null,"url":"https://ijcai.org/proceedings/2007/78","pdf":"https://ijcai.org/proceedings/2007/0078.pdf","markdown":"https://ijcai.org/proceedings/2007/78.md","bibtex":"https://ijcai.org/proceedings/2007/bibtex/78","volume":{"slug":"2007","title":"Proceedings of the Twentieth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2007","url":"https://ijcai.org/proceedings/2007/","year":2007,"location":"Hyderabad, India","dates":"","editors":"Ramon López de Mántaras","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":78,"pages":{"first":495,"last":499},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}