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On Singleton Arc Consistency for CSPs Defined by Monotone Patterns

Authors Clément Carbonnel, David A. Cohen, Martin C. Cooper, Stanislav Zivny

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Clément Carbonnel
David A. Cohen
Martin C. Cooper
Stanislav Zivny

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Clément Carbonnel, David A. Cohen, Martin C. Cooper, and Stanislav Zivny. On Singleton Arc Consistency for CSPs Defined by Monotone Patterns. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 19:1-19:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.STACS.2018.19

Abstract

Singleton arc consistency is an important type of local consistency which has been recently shown to solve all constraint satisfaction problems (CSPs) over constraint languages of bounded width. We aim to characterise all classes of CSPs defined by a forbidden pattern that are solved by singleton arc consistency and closed under removing constraints. We identify five new patterns whose absence ensures solvability by singleton arc consistency, four of which are provably maximal and three of which generalise 2-SAT. Combined with simple counter-examples for other patterns, we make significant progress towards a complete classification.

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Keywords
  • constraint satisfaction problems
  • forbidden patterns
  • singleton arc consistency

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References

  1. Albert Atserias, Andrei A. Bulatov, and Víctor Dalmau. On the power of k -consistency. In Lars Arge, Christian Cachin, Tomasz Jurdzinski, and Andrzej Tarlecki, editors, Automata, Languages and Programming, 34th International Colloquium, ICALP 2007, Wroclaw, Poland, July 9-13, 2007, Proceedings, volume 4596 of Lecture Notes in Computer Science, pages 279-290. Springer, 2007. URL: http://dx.doi.org/10.1007/978-3-540-73420-8_26.
  2. Libor Barto and Marcin Kozik. Constraint satisfaction problems solvable by local consistency methods. J. ACM, 61(1):3:1-3:19, 2014. URL: http://dx.doi.org/10.1145/2556646.
  3. Nicolas Beldiceanu, Mats Carlsson, and Jean-Xavier Rampon. Global Constraint Catalog, 2017. URL: http://sofdem.github.io/gccat/gccat/titlepage.html.
  4. Joel Berman, Paweł Idziak, Petar Marković, Ralph McKenzie, Matthew Valeriote, and Ross Willard. Varieties with few subalgebras of powers. Transactions of the American Mathematical Society, 362(3):1445-1473, 2010. URL: http://dx.doi.org/10.1090/S0002-9947-09-04874-0.
  5. Christian Bessiere and Romuald Debruyne. Theoretical analysis of singleton arc consistency and its extensions. Artif. Intell., 172(1):29-41, 2008. URL: http://dx.doi.org/10.1016/j.artint.2007.09.001.
  6. Christian Bessière, Jean-Charles Régin, Roland H. C. Yap, and Yuanlin Zhang. An optimal coarse-grained arc consistency algorithm. Artif. Intell., 165(2):165-185, 2005. URL: http://dx.doi.org/10.1016/j.artint.2005.02.004.
  7. Sally C. Brailsford, Chris N. Potts, and Barbara M. Smith. Constraint satisfaction problems: Algorithms and applications. European Journal of Operational Research, 119(3):557-581, 1999. URL: http://dx.doi.org/10.1016/S0377-2217(98)00364-6.
  8. Andrei Bulatov. Bounded relational width, 2009. Unpublished manuscript. Google Scholar
  9. Andrei A. Bulatov. A dichotomy theorem for nonuniform csps. In Chris Umans, editor, 58th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2017, Berkeley, CA, USA, October 15-17, 2017, pages 319-330. IEEE Computer Society, 2017. URL: http://dx.doi.org/10.1109/FOCS.2017.37.
  10. Andrei A. Bulatov and Víctor Dalmau. A simple algorithm for mal'tsev constraints. SIAM J. Comput., 36(1):16-27, 2006. URL: http://dx.doi.org/10.1137/050628957.
  11. Andrei A. Bulatov, Peter Jeavons, and Andrei A. Krokhin. Classifying the complexity of constraints using finite algebras. SIAM J. Comput., 34(3):720-742, 2005. URL: http://dx.doi.org/10.1137/S0097539700376676.
  12. Clément Carbonnel, David A. Cohen, Martin C. Cooper, and Stanislav Zivny. On singleton arc consistency for CSPs defined by monotone patterns, April 2017. URL: http://arxiv.org/abs/1704.06215.
  13. Hubie Chen, Víctor Dalmau, and Berit Grußien. Arc consistency and friends. J. Log. Comput., 23(1):87-108, 2013. URL: http://dx.doi.org/10.1093/logcom/exr039.
  14. Cheng-Chung Cheng and Stephen F. Smith. Applying constraint satisfaction techniques to job shop scheduling. Annals of Operations Research, 70(0):327-357, 1997. URL: http://dx.doi.org/10.1023/A:1018934507395.
  15. David A. Cohen, Martin C. Cooper, Páidí Creed, Dániel Marx, and András Z. Salamon. The tractability of CSP classes defined by forbidden patterns. J. Artif. Intell. Res., 45:47-78, 2012. URL: http://dx.doi.org/10.1613/jair.3651.
  16. David A. Cohen, Martin C. Cooper, Guillaume Escamocher, and Stanislav Zivny. Variable and value elimination in binary constraint satisfaction via forbidden patterns. J. Comput. Syst. Sci., 81(7):1127-1143, 2015. URL: http://dx.doi.org/10.1016/j.jcss.2015.02.001.
  17. David A. Cohen and Peter G. Jeavons. The power of propagation: when GAC is enough. Constraints, 22(1):3-23, 2017. URL: http://dx.doi.org/10.1007/s10601-016-9251-0.
  18. Martin C. Cooper, David A. Cohen, and Peter Jeavons. Characterising tractable constraints. Artif. Intell., 65(2):347-361, 1994. URL: http://dx.doi.org/10.1016/0004-3702(94)90021-3.
  19. Martin C. Cooper, Aymeric Duchein, Achref El Mouelhi, Guillaume Escamocher, Cyril Terrioux, and Bruno Zanuttini. Broken triangles: From value merging to a tractable class of general-arity constraint satisfaction problems. Artif. Intell., 234:196-218, 2016. URL: http://dx.doi.org/10.1016/j.artint.2016.02.001.
  20. Martin C. Cooper and Guillaume Escamocher. Characterising the complexity of constraint satisfaction problems defined by 2-constraint forbidden patterns. Discrete Applied Mathematics, 184:89-113, 2015. URL: http://dx.doi.org/10.1016/j.dam.2014.10.035.
  21. Martin C. Cooper, Peter G. Jeavons, and András Z. Salamon. Generalizing constraint satisfaction on trees: Hybrid tractability and variable elimination. Artif. Intell., 174(9-10):570-584, 2010. URL: http://dx.doi.org/10.1016/j.artint.2010.03.002.
  22. Martin C. Cooper and Stanislav Zivny. Hybrid tractability of valued constraint problems. Artif. Intell., 175(9-10):1555-1569, 2011. URL: http://dx.doi.org/10.1016/j.artint.2011.02.003.
  23. Martin C. Cooper and Stanislav Zivny. The power of arc consistency for csps defined by partially-ordered forbidden patterns. In Martin Grohe, Eric Koskinen, and Natarajan Shankar, editors, Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science, LICS '16, New York, NY, USA, July 5-8, 2016, pages 652-661. ACM, 2016. URL: http://dx.doi.org/10.1145/2933575.2933587.
  24. Eugene C. Freuder. A sufficient condition for backtrack-free search. J. ACM, 29(1):24-32, 1982. URL: http://dx.doi.org/10.1145/322290.322292.
  25. Eugene C. Freuder. Eliminating Interchangeable Values in Constraint Satisfaction Problems. In Proceedings of AAAI-91, pages 227-233, 1991. URL: http://www.aaai.org/Library/AAAI/1991/aaai91-036.php.
  26. Martin Grohe. The complexity of homomorphism and constraint satisfaction problems seen from the other side. J. ACM, 54(1):1:1-1:24, 2007. URL: http://dx.doi.org/10.1145/1206035.1206036.
  27. Pawel M. Idziak, Petar Markovic, Ralph McKenzie, Matthew Valeriote, and Ross Willard. Tractability and learnability arising from algebras with few subpowers. SIAM J. Comput., 39(7):3023-3037, 2010. URL: http://dx.doi.org/10.1137/090775646.
  28. Marcin Kozik. Weak consistency notions for all the csps of bounded width. In Martin Grohe, Eric Koskinen, and Natarajan Shankar, editors, Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science, LICS '16, New York, NY, USA, July 5-8, 2016, pages 633-641. ACM, 2016. URL: http://dx.doi.org/10.1145/2933575.2934510.
  29. Norman Lim, Shikharesh Majumdar, and Peter Ashwood-Smith. A constraint programming-based resource management technique for processing mapreduce jobs with slas on clouds. In 43rd International Conference on Parallel Processing, ICPP 2014, Minneapolis, MN, USA, September 9-12, 2014, pages 411-421. IEEE Computer Society, 2014. URL: http://dx.doi.org/10.1109/ICPP.2014.50.
  30. Roger Mohr and Thomas C. Henderson. Arc and path consistency revisited. Artif. Intell., 28(2):225-233, 1986. URL: http://dx.doi.org/10.1016/0004-3702(86)90083-4.
  31. Cemalettin Ozturk and M. Arslan Ornek. Optimisation and constraint based heuristic methods for advanced planning and scheduling systems. International Journal of Industrial Engineering: Theory, Applications and Practice, 23(1):26-48, 2016. URL: http://journals.sfu.ca/ijietap/index.php/ijie/article/view/1930.
  32. Pinar Senkul and Ismail Hakki Toroslu. An architecture for workflow scheduling under resource allocation constraints. Inf. Syst., 30(5):399-422, 2005. URL: http://dx.doi.org/10.1016/j.is.2004.03.003.
  33. Dmitriy Zhuk. A proof of CSP dichotomy conjecture. In Chris Umans, editor, 58th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2017, Berkeley, CA, USA, October 15-17, 2017, pages 331-342. IEEE Computer Society, 2017. URL: http://dx.doi.org/10.1109/FOCS.2017.38.
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