{"type":"ScholarlyArticle","title":"Solving Sudoku with Consistency: A Visual and Interactive Approach","authors":[{"name":"Ian Howell","slug":"ian-howell","given":"Ian","family":"Howell","affiliation":"Constraint Systems Laboratory , University of Nebraska-Lincoln , USA"},{"name":"Robert Woodward","slug":"robert-woodward","given":"Robert","family":"Woodward","affiliation":"Constraint Systems Laboratory , University of Nebraska-Lincoln , USA; CNRS , University of Montpellier , France"},{"name":"Berthe Y. Choueiry","slug":"berthe-y-choueiry","given":"Berthe Y.","family":"Choueiry","affiliation":"Constraint Systems Laboratory , University of Nebraska-Lincoln , USA"},{"name":"Christian Bessiere","slug":"christian-bessiere","given":"Christian","family":"Bessiere","affiliation":"CNRS , University of Montpellier , France"}],"abstract":"We describe an online, interactive system with a\r\ngraphical interface to illustrate the power and operation\r\nof consistency algorithms in a friendly and\r\npopular context, namely, solving Sudoku puzzles.\r\nOur tool implements algorithms for enforcing five\r\n(domain-based) consistency properties on binary\r\nand non-binary constraint models. Our tool is useful\r\nfor research, education, and outreach. From\r\na scientific standpoint, we propose a new consistency\r\nproperty that can solve the hardest known\r\n9×9 Sudoku instances without search, but leave\r\nopen the question of the lowest level of consistency\r\nneeded to solve every 9×9 Sudoku puzzle. We\r\nhave used the current tool and its predecessor in the\r\nclassroom to introduce students to modeling problems\r\nwith constraints, explain consistency properties,\r\nand illustrate the operations of constraint propagation\r\nand lookahead. Finally, we have also used\r\nthis tool during outreach activities to demystify AI\r\nto children and the general public and show them\r\nhow computers think.","doi":"10.24963/ijcai.2018/852","url":"https://ijcai.org/proceedings/2018/852","pdf":"https://ijcai.org/proceedings/2018/0852.pdf","markdown":"https://ijcai.org/proceedings/2018/852.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/852","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":"Demos","track":"Demos","number":852,"pages":{"first":5829,"last":5831},"keywords":["Constraints and Satisfiability: Constraint Satisfaction","Multidisciplinary Topics and Applications: Human-Computer Interaction"],"videos":[],"references":[{"position":1,"raw":"[Bennaceur and Affane, 2001] Hachemi Bennaceur and Mohamed-Salah Affane. Partition-k-AC: An Efficient Filtering Technique Combining Domain Partition and Arc Consistency. In Principles and Practice of Constraint Programming (CP 01), volume 2239 of LNCS, pages 560-564. Springer, 2001.","title":"Hachemi Bennaceur and Mohamed-Salah Affane. Partition-k-AC: An Efficient Filtering Technique Combining Domain Partition and Arc Consistency","authors":"Affane Bennaceur","year":"2001","venue":"Principles and Practice of Constraint Programming (CP 01)","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Bessiere and Debruyne, 2008] Christian Bessiere and Ro- muald Debruyne. Theoretical analysis of singleton arc consistency and its extensions. Artificial Intelligence, 172(1):29-41, 2008.","title":"Christian Bessiere and Romuald Debruyne. Theoretical analysis of singleton arc consistency and its extensions","authors":"Debruyne Bessiere","year":"2008","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Debruyne and Bessiere, 1997] Romuald Debruyne and Christian Bessiere. Some practicable filtering techniques for the constraint satisfaction problem. In In Proceedings of IJCAI'97, pages 412-417, 1997.","title":"Some practicable filtering techniques for the constraint satisfaction problem","authors":"Romuald Debruyne, Christian Bessiere","year":"1997","venue":"Proceedings of IJCAI'97","doi":null,"url":null,"internal_url":"/proceedings/1997/61"},{"position":4,"raw":"[Mackworth, 1977] Alan K. Mackworth. Consistency in Networks of Relations. Artificial Intelligence, 8:99-118, 1977.","title":"Consistency in Networks of Relations","authors":"Alan K Mackworth","year":"1977","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Reeson et al., 2007] Christopher G. Reeson, Kai-Chen Huang, Kenneth M. Bayer, and Berthe Y. Choueiry. An Interactive Constraint-Based Approach to Sudoku. In Pro- ceedings of AAAI-2007, pages 1976-1977, 2007.","title":"An Interactive Constraint-Based Approach to Sudoku","authors":"G Christopher, Kai-Chen Reeson, Kenneth M Huang, Berthe Y Bayer, Choueiry","year":"2007","venue":"Proceedings of AAAI-2007","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Régin, 1994] Jean-Charles Régin. A filtering algorithm for constraints of difference in constraint satisfaction prob- lems. In Proceedings of AAAI-94, pages 362-437, Seattle, WA, 1994.","title":"A filtering algorithm for constraints of difference in constraint satisfaction problems","authors":"Jean-Charles Régin","year":"1994","venue":"Proceedings of AAAI-94","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Simonis, 2005] Helmut Simonis. Sudoku as a constraint problem. In Proceedings of the Fifth International Work- shop on Modeling and Reformulating Constraint Satisfac- tion Problems, pages 13-27, 2005.","title":"Sudoku as a constraint problem","authors":"Helmut Simonis","year":"2005","venue":"Proceedings of the Fifth International Workshop on Modeling and Reformulating Constraint Satisfaction Problems","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Waltz, 1975] David Waltz. Understanding Line Drawings of Scenes with Shadows. In P.H. Winston, editor, The Psy- chology of Computer Vision, pages 19-91.","title":"Understanding Line Drawings of Scenes with Shadows","authors":"David Waltz","year":null,"venue":"The Psychology of Computer Vision","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Yato, 2003] Takayuki Yato. Complexity and Completeness of Finding Another Solution and its Application to Puz- zles. Master's thesis, University of Tokyo, 2003.","title":"Complexity and Completeness of Finding Another Solution and its Application to Puzzles","authors":"Takayuki Yato","year":"2003","venue":null,"doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}