{"type":"ScholarlyArticle","title":"Bipartite Encoding: A New Binary Encoding for Solving Non-Binary CSPs","authors":[{"name":"Ruiwei Wang","slug":"ruiwei-wang","given":"Ruiwei","family":"Wang","affiliation":"School of Computing , National University of Singapore"},{"name":"Roland H.C. Yap","slug":"roland-h-c-yap","given":"Roland H.C.","family":"Yap","affiliation":"School of Computing , National University of Singapore"}],"abstract":"Constraint Satisfaction Problems (CSPs) are typically solved with Generalized Arc Consistency (GAC). A general CSP can also be encoded into a binary CSP and solved with Arc Consistency (AC). The well-known Hidden Variable Encoding (HVE) is still a state-of-the-art binary encoding for solving CSPs. We propose a new binary encoding, called Bipartite Encoding (BE) which uses the idea of partitioning constraints. A BE encoded CSP can achieve a higher level of consistency than GAC on the original CSP. We give an algorithm for creating compact bipartite encoding for non-binary CSPs. We present a AC propagator on the binary constraints from BE exploiting their special structure. Experiments on a large set of non-binary CSP benchmarks with table constraints using the Wdeg, Activity and Impact heuristics show that BE with our AC propagator can outperform existing state-of-the-art GAC algorithms (CT, STRbit) and binary encodings (HVE with HTAC).","doi":"10.24963/ijcai.2020/165","url":"https://ijcai.org/proceedings/2020/165","pdf":"https://ijcai.org/proceedings/2020/0165.pdf","markdown":"https://ijcai.org/proceedings/2020/165.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/165","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":165,"pages":{"first":1184,"last":1191},"keywords":["Constraints and SAT: Constraint Satisfaction","Constraints and SAT: Constraints: Modeling, Solvers, Applications"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/25392/file_25392.m3u8","length_sec":271,"provider":"hls"}],"references":[{"position":1,"raw":"[Bessiere et al., 2008] Christian Bessiere, Kostas Stergiou, and Toby Walsh. Domain filtering consistencies for non- binary constraints. Artificial Intelligence, 172(6-7):800- 822, 2008.","title":"Domain filtering consistencies for nonbinary constraints","authors":"Bessiere","year":"2008","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Boussemart et al., 2004] Frédéric Boussemart, Fred Hemery, Christophe Lecoutre, and Lakhdar Sais. Boost- ing systematic search by weighting constraints. In European Conference on Artificial Intelligence, 2004.","title":"Boosting systematic search by weighting constraints","authors":"Frédéric Boussemart, Fred Hemery, Christophe Lecoutre, Lakhdar Sais","year":"2004","venue":"European Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Briggs and Torczon, 1993] Preston Briggs and Linda Torc- zon. An efficient representation for sparse sets. ACM Let- ters on Programming Languages and Systems (LOPLAS), 2(1-4):59-69, 1993.","title":"An efficient representation for sparse sets","authors":"Preston Briggs, Linda Torczon","year":"1993","venue":"ACM Letters on Programming Languages and Systems (LOPLAS)","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Dechter and Pearl, 1989] Rina Dechter and Judea Pearl. Tree clustering for constraint networks. Artificial Intel- ligence, 38(3):353-366, 1989.","title":"Tree clustering for constraint networks","authors":"Rina Dechter, Judea Pearl","year":"1989","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Demeulenaere et al., 2016] Jordan Demeulenaere, Renaud Hartert, Christophe Lecoutre, Guillaume Perez, Laurent Perron, Jean-Charles Régin, and Pierre Schaus. Compact- Table: efficiently filtering table constraints with reversible sparse bit-sets. In International Conference on Principles and Practice of Constraint Programming, 2016.","title":"Compact-Table: efficiently filtering table constraints with reversible sparse bit-sets","authors":"Jordan Demeulenaere, Renaud Hartert, Christophe Lecoutre, Guillaume Perez, Laurent Perron, Jean-Charles Régin, Pierre Schaus","year":"2016","venue":"International Conference on Principles and Practice of Constraint Programming","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Dolan and Moré, 2002] Elizabeth D Dolan and Jorge J Moré. Benchmarking optimization software with perfor- mance profiles. Mathematical programming, 91(2):201- 213, 2002.","title":"Benchmarking optimization software with performance profiles","authors":"D Elizabeth, Jorge J Dolan, Moré","year":"2002","venue":"Mathematical programming","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Janssen et al., 1989] Philippe Janssen, Philippe Jégou, Bernard Nouguier, and Marie-Catherine Vilarem. A fil- tering process for general constraint-satisfaction problems: achieving pairwise-consistency using an associated binary representation. In IEEE International Workshop on Tools for Artificial Intelligence, 1989.","title":"A filtering process for general constraint-satisfaction problems: achieving pairwise-consistency using an associated binary representation","authors":"Philippe Janssen, Philippe Jégou, Bernard Nouguier, Marie-Catherine Vilarem","year":"1989","venue":"IEEE International Workshop on Tools for Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Lecoutre and Szymanek, 2006] Christophe Lecoutre and Radoslaw Szymanek. Generalized arc consistency for pos- itive table constraints. In International Conference on Principles and Practice of Constraint Programming, 2006.","title":"Generalized arc consistency for positive table constraints","authors":"Christophe Lecoutre, Radoslaw Szymanek","year":"2006","venue":"International Conference on Principles and Practice of Constraint Programming","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Lecoutre and Vion, 2008] Christophe Lecoutre and Julien Vion. Enforcing arc consistency using bitwise operations. Constraint Programming Letters, 2:21-35, 2008.","title":"Enforcing arc consistency using bitwise operations","authors":"Christophe Lecoutre, Julien Vion","year":"2008","venue":"Constraint Programming Letters","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Lecoutre et al., 2012] Christophe Lecoutre, Chavalit Likit- vivatanavong, and Roland H.C. Yap. A path-optimal GAC algorithm for table constraints. In European Conference on Artificial Intelligence, 2012.","title":"A path-optimal GAC algorithm for table constraints","authors":"Christophe Lecoutre, Chavalit Likitvivatanavong, Roland H C Yap","year":"2012","venue":"European Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Lecoutre et al., 2013] Christophe Lecoutre, Anastasia Pa- parrizou, and Kostas Stergiou. Extending STR to a higher- order consistency. In AAAI Conference on Artificial Intel- ligence, 2013.","title":"Extending STR to a higherorder consistency","authors":"Christophe Lecoutre, Anastasia Paparrizou, Kostas Stergiou","year":"2013","venue":"AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Lecoutre, 2011] Christophe Lecoutre. STR2: optimized simple tabular reduction for table constraints. Constraints, 16(4):341-371, 2011.","title":"STR2: optimized simple tabular reduction for table constraints","authors":"Christophe Lecoutre","year":"2011","venue":"Constraints","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Likitvivatanavong et al., 2014] Chavalit Likitvivatanavong, Wei Xia, and Roland H.C. Yap. Higher-order consisten- cies through GAC on factor variables. In International Conference on Principles and Practice of Constraint Pro- gramming, 2014.","title":"Higher-order consistencies through GAC on factor variables","authors":"Chavalit Likitvivatanavong, Wei Xia, Roland H C Yap","year":"2014","venue":"International Conference on Principles and Practice of Constraint Programming","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Michel and Van Hentenryck, 2012] Laurent Michel and Pascal Van Hentenryck. Activity-based search for black- box constraint programming solvers. In International Conference on Integration of Artificial Intelligence and Operations Research Techniques in Constraint Programming, 2012.","title":"Activity-based search for blackbox constraint programming solvers","authors":"Van Michel, Laurent Hentenryck, Pascal Michel, Van Hentenryck","year":"2012","venue":"International Conference on Integration of Artificial Intelligence and Operations Research Techniques in Constraint Programming","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Refalo, 2004] Philippe Refalo. Impact-based search strate- gies for constraint programming. In International Confer- ence on Principles and Practice of Constraint Program- ming, 2004.","title":"Impact-based search strategies for constraint programming","authors":"Philippe Refalo","year":"2004","venue":"International Conference on Principles and Practice of Constraint Programming","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Rossi et al., 1990] Francesca Rossi, Charles J Petrie, and Vasant Dhar. On the equivalence of constraint satisfaction problems. In European Conference on Artificial Intelli- gence, 1990.","title":"On the equivalence of constraint satisfaction problems","authors":"Francesca Rossi, Charles J Petrie, Vasant Dhar","year":"1990","venue":"European Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Samaras and Stergiou, 2005] Nikolaos Samaras and Kostas Stergiou. Binary encodings of non-binary constraint sat- isfaction problems: Algorithms and experimental results. Journal of Artificial Intelligence Research, 24:641-684, 2005.","title":"Binary encodings of non-binary constraint satisfaction problems: Algorithms and experimental results","authors":"Stergiou ; ] Nikolaos Samaras, Kostas Samaras, Stergiou","year":"2005","venue":"Journal of Artificial Intelligence Research","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Schneider and Choueiry, 2018] Anthony Schneider and Berthe Y Choueiry. PW-CT: extending Compact-Table to enforce pairwise consistency on table constraints. In International Conference on Principles and Practice of Constraint Programming, 2018.","title":"PW-CT: extending Compact-Table to enforce pairwise consistency on table constraints","authors":"Anthony Schneider, Berthe Y Choueiry","year":"2018","venue":"International Conference on Principles and Practice of Constraint Programming","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Smith and Grant, 1998] Barbara M Smith and Stuart A Grant. Trying harder to fail first. In European Conference on Artificial Intelligence, 1998.","title":"Trying harder to fail first","authors":"M Barbara, Stuart A Smith, Grant","year":"1998","venue":"European Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Stergiou and Walsh, 1999] Kostas Stergiou and Toby Walsh. Encodings of non-binary constraint satisfac- tion problems. In National Conference on Artificial Intelligence, 1999.","title":"Encodings of non-binary constraint satisfaction problems","authors":"Walsh ; Stergiou, Kostas Stergiou, Toby Walsh","year":"1999","venue":"National Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Verhaeghe et al., 2018] Hélene Verhaeghe, Christophe Lecoutre, and Pierre Schaus. Compact-MDD: Efficiently filtering (s)MDD constraints with reversible sparse bit-sets. In International Joint Conference on Artificial Intelligence, 2018.","title":"Compact-MDD: Efficiently filtering (s)MDD constraints with reversible sparse bit-sets","authors":"Verhaeghe","year":"2018","venue":"International Joint Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":"/proceedings/2018/192"},{"position":22,"raw":"[Verhaeghe et al., 2019] Hélène Verhaeghe, Christophe Lecoutre, and Pierre Schaus. Extending Compact- Diagram to basic smart multi-valued variable diagrams. In International Conference on Integration of Constraint Programming, Artificial Intelligence, and Operations Research, 2019.","title":"Extending Compact-Diagram to basic smart multi-valued variable diagrams","authors":"Hélène Verhaeghe, Christophe Lecoutre, Pierre Schaus","year":"2019","venue":"International Conference on Integration of Constraint Programming","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Wang and Yap, 2019] Ruiwei Wang and Roland H.C. Yap. Arc consistency revisited. In International Conference on Integration of Constraint Programming, Artificial Intelli- gence, and Operations Research, 2019.","title":"Arc consistency revisited","authors":"Wang, Yap ; ] Ruiwei Wang, Roland H C Yap","year":"2019","venue":"International Conference on Integration of Constraint Programming","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Wang et al., 2016] Ruiwei Wang, Wei Xia, Roland H.C. Yap, and Zhanshan Li. Optimizing simple tabular reduc- tion with a bitwise representation. In International Joint Conference on Artificial Intelligence, 2016.","title":"Optimizing simple tabular reduction with a bitwise representation","authors":"Ruiwei Wang, Wei Xia, H C Roland, Zhanshan Yap, Li","year":"2016","venue":"International Joint Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":"/proceedings/2016/117"},{"position":25,"raw":"[Yap et al., 2020] Roland H.C. Yap, Wei Xia, and Ruiwei Wang. Generalized arc consistency algorithms for table constraints: A summary of algorithmic ideas. In AAAI Conference on Artificial Intelligence, 2020.","title":"Generalized arc consistency algorithms for table constraints: A summary of algorithmic ideas","authors":"H C Roland, Wei Yap, Ruiwei Xia, Wang","year":"2020","venue":"AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}