{"type":"ScholarlyArticle","title":"On the Kernelization of Global Constraints","authors":[{"name":"Clément Carbonnel","slug":"clement-carbonnel","given":"Clément","family":"Carbonnel","affiliation":"University of Oxford"},{"name":"Emmanuel Hebrard","slug":"emmanuel-hebrard","given":"Emmanuel","family":"Hebrard","affiliation":"CNRS , LAAS-CNRS , Université de Toulouse"}],"abstract":"Kernelization is a powerful concept from parameterized complexity theory that captures (a certain idea of) efficient polynomial-time preprocessing for hard decision problems. However, exploiting this technique in the context of constraint programming is challenging. Building on recent results for the VertexCover constraint, we introduce novel \"loss-less\" kernelization variants that are tailored for constraint propagation. We showcase the theoretical interest of our ideas on two constraints, VertexCover and EdgeDominatingSet.","doi":"10.24963/ijcai.2017/81","url":"https://ijcai.org/proceedings/2017/81","pdf":"https://ijcai.org/proceedings/2017/0081.pdf","markdown":"https://ijcai.org/proceedings/2017/81.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/81","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":"Constraints and Satisfiability","track":"Main track","number":81,"pages":{"first":578,"last":584},"keywords":["Knowledge Representation, Reasoning, and Logic: Computational Complexity of Reasoning","Constraints and Satisfiability: Constraints and Satisfiability","Constraints and Satisfiability: Global Constraints"],"videos":[],"references":[{"position":1,"raw":"[Abu-Khzam et al., 2007] Faisal N Abu-Khzam, Michael R Fellows, Michael A Langston, and W Henry Suters. Crown Structures for Vertex Cover Kernelization. Theory of Computing Systems, 41(3):411-430, 2007.","title":"Crown Structures for Vertex Cover Kernelization","authors":"Faisal N Abu-Khzam, Michael A Michael R Fellows, W Langston, Suters Henry","year":"2007","venue":"Theory of Computing Systems","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Bessiere et al., 2004] C. Bessiere, E. Hebrard, B. Hnich, and T. Walsh. The Complexity of Global Constraints. In Proceedings of the 19th National Conference on Artificial Intelligence (AAAI), pages 112-117, 2004.","title":"The Complexity of Global Constraints","authors":"C Bessiere, E Hebrard, B Hnich, T Walsh","year":"2004","venue":"Proceedings of the 19th National Conference on Artificial Intelligence (AAAI)","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Bessiere et al., 2006] C. Bessiere, E. Hebrard, B. Hnich, Z. Kiziltan, and T. Walsh. Filtering Algorithms for the NValue Constraint. Constraints, 11(4):271-293, 2006.","title":"Filtering Algorithms for the NValue Constraint","authors":"C Bessiere, E Hebrard, B Hnich, Z Kiziltan, T Walsh","year":"2006","venue":"Constraints","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Bessiere et al., 2008] Christian Bessiere, Emmanuel He- brard, Brahim Hnich, Zeynep Kiziltan, Claude-Guy Quim- per, and Toby Walsh. The Parameterized Complexity of Global Constraints. In Proceedings of the 23rd National Conference on Artificial Intelligence (AAAI), pages 235- 240, 2008.","title":"The Parameterized Complexity of Global Constraints","authors":"Bessiere","year":"2008","venue":"Proceedings of the 23rd National Conference on Artificial Intelligence (AAAI)","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Carbonnel and Hebrard, 2016] Clément Carbonnel and Em- manuel Hebrard. Propagation via Kernelization: the Ver- tex Cover Constraint. In Proceedings of the 22nd Inter- national Conference on Principles and Practice of Con- straint Programming (CP), pages 147-156, 2016.","title":"Propagation via Kernelization: the Vertex Cover Constraint","authors":"Hebrard Carbonnel, Clément Carbonnel, Emmanuel Hebrard","year":"2016","venue":"Proceedings of the 22nd International Conference on Principles and Practice of Constraint Programming (CP)","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Carbonnel, 2016] Clément Carbonnel. Harnessing tractability in constraint satisfaction problems. PhD thesis, Institut National Polytechnique de Toulouse, 2016.","title":"Harnessing tractability in constraint satisfaction problems","authors":"Clément Carbonnel","year":"2016","venue":null,"doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Chen et al., 2006] Jinaer Chen, Iyad A. Kanj, and Ge Xia. Improved Parameterized Upper Bounds for Vertex Cover. In Proceedings of the 31st International Symposium on Mathematical Foundations of Computer Science (MFCS), pages 238-249, 2006.","title":"Improved Parameterized Upper Bounds for Vertex Cover","authors":"Chen","year":"2006","venue":"Proceedings of the 31st International Symposium on Mathematical Foundations of Computer Science (MFCS)","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Chlebík and Chlebíková, 2008] Miroslav Chlebík and Janka Chlebíková. Crown reductions for the Minimum Weighted Vertex Cover problem. Discrete Applied Mathematics, 156(3):292-312, 2008.","title":"Miroslav Chlebík and Janka Chlebíková. Crown reductions for the Minimum Weighted Vertex Cover problem","authors":"Chlebíková Chlebík","year":"2008","venue":"Discrete Applied Mathematics","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Creignou et al., 2013] Nadia Creignou, Arne Meier, Julian- Steffen Müller, Johannes Schmidt, and Heribert Vollmer. Paradigms for Parameterized Enumeration. In Proceed- ings of the 31st International Symposium on Mathemati- cal Foundations of Computer Science (MFCS), pages 290- 301, 2013.","title":"Paradigms for Parameterized Enumeration","authors":"Nadia Creignou, Arne Meier, Julian-Steffen Müller, Johannes Schmidt, Heribert Vollmer","year":"2013","venue":"Proceedings of the 31st International Symposium on Mathematical Foundations of Computer Science (MFCS)","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Cygan et al., 2015] Marek Cygan, Fedor V Fomin, Łukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michał Pilipczuk, and Saket Saurabh. Parame- terized algorithms. Springer, 2015.","title":"Parameterized algorithms","authors":"Marek Cygan, Łukasz Fedor V Fomin, Daniel Kowalik, Dániel Lokshtanov, Marcin Marx, Michał Pilipczuk, Saket Pilipczuk, Saurabh","year":"2015","venue":null,"doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Damaschke, 2006] Peter Damaschke. Parameterized enu- meration, transversals, and imperfect phylogeny recon- struction. Theoretical Computer Science, 351(3):337-350, 2006.","title":"Parameterized enumeration, transversals, and imperfect phylogeny reconstruction","authors":"Peter Damaschke","year":"2006","venue":"Theoretical Computer Science","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Garey and Johnson, 1979] Michael Garey and David S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H.Freeman and Company, San Francisco, CA., 1979.","title":"Computers and Intractability: A Guide to the Theory of NP-Completeness","authors":"Michael Garey, David S Johnson","year":"1979","venue":null,"doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Gaspers and Szeider, 2011] Serge Gaspers and Stefan Szei- der. Kernels for Global Constraints. In Proceedings of the 22nd International Joint Conference on Artificial Intelli- gence (IJCAI), pages 540-545, 2011.","title":"Serge Gaspers and Stefan Szeider","authors":"Szeider Gaspers","year":"2011","venue":"Proceedings of the 22nd International Joint Conference on Artificial Intelligence (IJCAI)","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Hagerup, 2012] Torben Hagerup. Kernels for Edge Domi- nating Set: Simpler or Smaller. In Proceedings of the 31st International Symposium on Mathematical Foundations of Computer Science (MFCS), pages 491-502, 2012.","title":"Kernels for Edge Dominating Set: Simpler or Smaller","authors":"Torben Hagerup, Hagerup","year":"2012","venue":"Proceedings of the 31st International Symposium on Mathematical Foundations of Computer Science (MFCS)","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Harary, 1969] Frank Harary. Graph theory, 1969.","title":"Graph theory","authors":"Frank Harary","year":"1969","venue":null,"doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Lampis, 2011] Michael Lampis. A Kernel of Order 2k - c log k for Vertex Cover. Information Processing Letters, 111(23):1089-1091, 2011.","title":"A Kernel of Order 2kc log k for Vertex Cover","authors":"Michael Lampis","year":"2011","venue":"Information Processing Letters","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Nemhauser and Trotter Jr, 1975] George L Nemhauser and Leslie E Trotter Jr. Vertex packings: Structural properties and algorithms. Mathematical Programming, 8(1):232- 248, 1975.","title":"Vertex packings: Structural properties and algorithms","authors":"Trotter Nemhauser, ; ] Jr, L George, Leslie E Nemhauser, Trotter","year":"1975","venue":"Mathematical Programming","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Samer and Szeider, 2008] Marko Samer and Stefan Szeider. Backdoor trees. In Proceedings of the 23rd National Conference on Artificial Intelligence (AAAI), pages 13-17, 2008.","title":"Backdoor trees","authors":"Marko Samer, Stefan Szeider","year":"2008","venue":"Proceedings of the 23rd National Conference on Artificial Intelligence (AAAI)","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Yannakakis and Gavril, 1980] Mihalis Yannakakis and Fan- ica Gavril. Edge Dominating Sets in Graphs. SIAM J. Appl. Math., 38(3):364-372, 1980.","title":"Mihalis Yannakakis and Fanica Gavril. Edge Dominating Sets in Graphs","authors":"Gavril Yannakakis","year":"1980","venue":"SIAM J. Appl. Math","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}