{"type":"ScholarlyArticle","title":"Reasoning with Lines in the Euclidean Space","authors":[{"name":"Khalil Challita","slug":"khalil-challita","given":"Khalil","family":"Challita","affiliation":""}],"abstract":"The main result of this paper is to show that the problem of instantiating a finite and path-consistent constraint network of lines in the Euclidean space is NP-complete. Indeed, we already know that reasoning with lines in the Euclidean space is NP-hard. In order to prove that this problem is NP-complete, we first establish that a particular instance of this problem can be solved by a nondeterministic polynomial-time algorithm, and then we show that solving any finite and path-consistent constraint network of lines in the Euclidean space is at most as difficult as solving that instance.Khalil Raymond Challita","doi":null,"url":"https://ijcai.org/proceedings/2009/84","pdf":"https://ijcai.org/proceedings/2009/0084.pdf","markdown":"https://ijcai.org/proceedings/2009/84.md","bibtex":"https://ijcai.org/proceedings/2009/bibtex/84","volume":{"slug":"2009","title":"Proceedings of the Twenty-First International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2009","url":"https://ijcai.org/proceedings/2009/","year":2009,"location":"Pasadena, California, USA","dates":"","editors":"Hiroaki Kitano","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":84,"pages":{"first":462,"last":466},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}