{"type":"ScholarlyArticle","title":"Estimating the size of search trees by sampling with domain knowledge","authors":[{"name":"Gleb Belov","slug":"gleb-belov","given":"Gleb","family":"Belov","affiliation":"Faculty of Information Technology , Monash University , Clayton , Australia"},{"name":"Samuel Esler","slug":"samuel-esler","given":"Samuel","family":"Esler","affiliation":"Faculty of Information Technology , Monash University , Clayton , Australia"},{"name":"Dylan Fernando","slug":"dylan-fernando","given":"Dylan","family":"Fernando","affiliation":"Faculty of Information Technology , Monash University , Clayton , Australia"},{"name":"Pierre Le Bodic","slug":"pierre-le-bodic","given":"Pierre","family":"Le Bodic","affiliation":"Faculty of Information Technology , Monash University , Clayton , Australia"},{"name":"George L. Nemhauser","slug":"george-l-nemhauser","given":"George L.","family":"Nemhauser","affiliation":"School of Industrial and Systems Engineering , Georgia Institute of Technology , Atlanta , USA"}],"abstract":"We show how recently-defined abstract models of the Branch-and-Bound algorithm can be used to obtain information on how the nodes are distributed in B&B search trees. This can be directly exploited in the form of probabilities in a sampling algorithm given by Knuth that estimates the size of a search tree. This method reduces the offline estimation error by a factor of two on search trees from Mixed-Integer Programming instances.","doi":"10.24963/ijcai.2017/67","url":"https://ijcai.org/proceedings/2017/67","pdf":"https://ijcai.org/proceedings/2017/0067.pdf","markdown":"https://ijcai.org/proceedings/2017/67.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/67","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Combinatorial & Heuristic Search","track":"Main track","number":67,"pages":{"first":473,"last":479},"keywords":["Combinatorial & Heuristic Search: Combinatorial search/optimisation","Constraints and Satisfiability: Solvers and Tools"],"videos":[],"references":[{"position":1,"raw":"[Achterberg, 2007] T. 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