{"type":"ScholarlyArticle","title":"Early and Efficient Identification of Useless Constraint Propagation for Alldifferent Constraints","authors":[{"name":"Xizhe Zhang","slug":"xizhe-zhang","given":"Xizhe","family":"Zhang","affiliation":"School of Biomedical Engineering and Informatics , Nanjing Medical University , Nanjing , China; School of Computer Science and Engineering , Northeastern University , Shenyang , China"},{"name":"Jian Gao","slug":"jian-gao","given":"Jian","family":"Gao","affiliation":"College of Information Science and Technology , Dalian Maritime University , Dalian , China"},{"name":"Yizhi Lv","slug":"yizhi-lv","given":"Yizhi","family":"Lv","affiliation":"School of Computer Science and Engineering , Northeastern University , Shenyang , China"},{"name":"Weixiong Zhang","slug":"weixiong-zhang","given":"Weixiong","family":"Zhang","affiliation":"Department of Computer Science and Engineering , Washington University , St. Louis , MO , USA"}],"abstract":"Constraints propagation and backtracking are two basic techniques for solving constraint satisfaction problems (CSPs). During the search for a solution, the variable and value pairs that do not belong to any solution can be discarded by constraint propagation to ensure generalized arc consistency so as to avoid the fruitless search. However, constraint propagation is frequently invoked often with little effect on many CSPs. Much effort has been devoted to predicting when to invoke constraint propagation for solving a CSP; however, no effective approach has been developed for the alldifferent constraint. Here we present a novel theorem for identifying the edges in a value graph of alldifferent constraint whose removal can significantly reduce useless constraint propagation. We prove that if an alternating cycle exists for a prospectively removable edge that represents a variable-value assignment, the edge (and the assignment) can be discarded without constraint propagation. Based on this theorem, we developed a novel optimizing technique for early detection of useless constraint propagation which can be incorporated in any existing algorithm for alldifferent constraint. Our implementation of the new method achieved speedup by a factor of 1-5 over the state-of-art approaches on 93 benchmark problem instances in 8 domains. Furthermore, the new algorithm is scalable well and runs increasingly faster than the existing methods on larger problems.","doi":"10.24963/ijcai.2020/157","url":"https://ijcai.org/proceedings/2020/157","pdf":"https://ijcai.org/proceedings/2020/0157.pdf","markdown":"https://ijcai.org/proceedings/2020/157.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/157","volume":{"slug":"2020","title":"Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2020","url":"https://ijcai.org/proceedings/2020/","year":2020,"location":"Yokohama","dates":"January 2021 (postponed from 11-17 July 2020)","editors":"Christian Bessiere","isbn":"978-0-9992411-6-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2020"},"section":"Constraints and SAT","track":"Main track","number":157,"pages":{"first":1126,"last":1133},"keywords":["Constraints and SAT: Constraints: Modeling, Solvers, Applications","Constraints and SAT: Global Constraints","Constraints and SAT: Constraint Satisfaction"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/25488/file_25488.m3u8","length_sec":296,"provider":"hls"}],"references":[{"position":1,"raw":"function Strongconnect(v)","title":"function Strongconnect","authors":null,"year":null,"venue":null,"doi":null,"url":null,"internal_url":null},{"position":2,"raw":"DFS[v] ← index; lowLink[v] ← index; index ← index + 1;","title":null,"authors":"Dfs","year":null,"venue":null,"doi":null,"url":null,"internal_url":null},{"position":3,"raw":"S.push(v);","title":null,"authors":"S Push","year":null,"venue":null,"doi":null,"url":null,"internal_url":null},{"position":4,"raw":"addCycles (lowLink[w], index-1)","title":null,"authors":"Addcycles","year":null,"venue":null,"doi":null,"url":null,"internal_url":null},{"position":5,"raw":"while inCycles(DE.top()) = true do","title":"true do","authors":null,"year":null,"venue":"while inCycles","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"pop nodes before v and pop v from S, add them to SCCs as an SCC; unconnected←true;","title":"pop nodes before v and pop v from S, add","authors":null,"year":null,"venue":null,"doi":null,"url":null,"internal_url":null},{"position":7,"raw":"if unconnected = false and DE is empty then","title":"and DE is empty then","authors":null,"year":null,"venue":null,"doi":null,"url":null,"internal_url":null},{"position":8,"raw":"for each pair (a', b') ∈cycles 25. if interval [a, b] is overlapped with interval [a',b'] then","title":"for each pair (a', b') ∈cycles 25. if interval [a, b","authors":null,"year":null,"venue":null,"doi":null,"url":null,"internal_url":null},{"position":9,"raw":"a'←min(a',a) and b'←max(b',b); 27. return 28. cycles.push(a, b) 29. return","title":"a'←min(a',a) and b'←max","authors":null,"year":null,"venue":null,"doi":null,"url":null,"internal_url":null},{"position":10,"raw":"function inCycles (e(a,b))","title":"function inCycles","authors":null,"year":null,"venue":null,"doi":null,"url":null,"internal_url":null},{"position":11,"raw":"for each pair (a', b') ∈cycles 32. if both DFS[a] and DFS[b] are in the interval [a', b'] then 33. return true 34. return false References","title":"for each pair (a', b') ∈cycles 32. if both DFS[a] and DFS[b","authors":null,"year":null,"venue":null,"doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Apt, 1998] Apt, Krzysztof R. 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