{"type":"ScholarlyArticle","title":"A Scalable Scheme for Counting Linear Extensions","authors":[{"name":"Topi Talvitie","slug":"topi-talvitie","given":"Topi","family":"Talvitie","affiliation":"University of Helsinki"},{"name":"Kustaa Kangas","slug":"kustaa-kangas","given":"Kustaa","family":"Kangas","affiliation":"Aalto University"},{"name":"Teppo Niinimäki","slug":"teppo-niinimaki","given":"Teppo","family":"Niinimäki","affiliation":"Aalto University"},{"name":"Mikko Koivisto","slug":"mikko-koivisto","given":"Mikko","family":"Koivisto","affiliation":"University of Helsinki"}],"abstract":"Counting the linear extensions of a given partial order not only has several applications in artificial intelligence but also represents a hard problem that challenges modern paradigms for approximate counting. Recently, Talvitie et al. (AAAI 2018) showed that an exponential time scheme beats the fastest known polynomial time schemes in practice, even if allowing hours of running time. Here, we present a novel scheme, relaxation Tootsie Pop, which in our experiments exhibits polynomial characteristics and significantly outperforms previous schemes. We also instantiate state-of-the-art model counters for CNF formulas; two natural encodings yield schemes that, however, are inferior to the more specialized schemes.","doi":"10.24963/ijcai.2018/710","url":"https://ijcai.org/proceedings/2018/710","pdf":"https://ijcai.org/proceedings/2018/0710.pdf","markdown":"https://ijcai.org/proceedings/2018/710.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/710","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Uncertainty in AI","track":"Main track","number":710,"pages":{"first":5119,"last":5125},"keywords":["Heuristic Search and Game Playing: Combinatorial Search and Optimisation","Constraints and SAT: SAT: Applications","Uncertainty in AI: Bayesian Networks","Uncertainty in AI: Approximate Probabilistic Inference"],"videos":[],"references":[{"position":1,"raw":"[Atkinson, 1990] Mike D. 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