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Bounds of graph parameters for global constraints

Published online by Cambridge University Press:  14 February 2007

Nicolas Beldiceanu ,
Thierry Petit  and
Guillaume Rochart
Nicolas Beldiceanu
Affiliation:
École des Mines de Nantes, LINA FRE CNRS 2729, 44307 Nantes, France; [email protected]; [email protected]
Thierry Petit
Affiliation:
École des Mines de Nantes, LINA FRE CNRS 2729, 44307 Nantes, France; [email protected]; [email protected]
Guillaume Rochart
Affiliation:
Bouygues e-lab, 78061 St Quentin en Yvelines, France; [email protected]
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Abstract

This article presents a basic scheme for deriving systematicallya filtering algorithm from the graph properties based representationof global constraints. This scheme is based on thebounds of the graph parameters used in the description ofa global constraint. The article provides bounds for the most commonused graph parameters.

Keywords

Global constraintgraph constraintfilteringbound.
Type
Research Article
Information
RAIRO - Operations Research , Volume 40 , Issue 4: Journées Francophones de Programmation par Contraintes 2005 , October 2006 , pp. 327 - 353
Copyright
© EDP Sciences, 2007

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References

P. Baptiste, C. Le Pape and L. Peridy, Global Constraints for Partial CSPs: A Case-Study of Resource and Due Date Constraints, in Principles and Practice of Constraint Programming (CP'98), edited by M. Maher and J.-F. Puget, Springer-Verlag, Lect. Notes Comput. Sci. 1520 (1998) 87–101.
N. Beldiceanu, Global Constraints as Graph Properties on a Structured Network of Elementary Constraints of the Same Type, in Principles and Practice of Constraint Programming (CP'2000), edited by R. Dechter, Springer-Verlag, Lect. Notes Comput. Sci. 1894 (2000) 52–66. Preprint available as SICS Tech Report T2000-01.
N. Beldiceanu, Global Constraints as Graph Properties on Structured Network of Elementary Constraints of the Same Type. Technical Report T2000-01, Swedish Institute of Computer Science (2000).
N. Beldiceanu, M. Carlsson and T. Petit, Deriving Filtering Algorithms from Constraint Checkers, in Principles and Practice of Constraint Programming (CP'2004), edited by M. Wallace, Springer-Verlag, Lect. Notes Comput. Sci. 3258 (2004) 107–122. Preprint available as SICS Tech Report T2004-08.
N. Beldiceanu, M. Carlsson and J.-X. Rampon, Global Constraint Catalog. Technical Report T2005-08, Swedish Institute of Computer Science (2005).
N. Beldiceanu and T. Petit, Cost Evaluation of Soft Global Constraints, in Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimisation Problems (CP-AI-OR 2004), edited by J.-C. Régin and M. Rueher, Springer-Verlag, Lect. Notes Comput. Sci. 3011 (2004) 80–95. CrossRef
C. Bessière, E. Hebrard, B. Hnich, Z. Kızıltan and T. Walsh, Filtering Algorithms for the nvalue Constraint, in International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CP-AI-OR'05), Prague, Czech Republic, edited by R. Barták and M. Milano, Springer-Verlag, Lect. Notes Comput. Sci. 3524 (2005) 79–93
C. Bessière and P. Van Hentenryck, To Be or not to Be... a Global Constraint, in Principles and Practice of Constraint Programming (CP'2003), edited by F. Rossi, Springer-Verlag, Lect. Notes Comput. Sci. 2833 (2003) 789–794. CrossRef
C. Bessière and J.-C. Régin, Refining the Basic Constraint Propagation Algorithm, in Proceedings of the Seventeenth International Joint Conference on Artificial Intelligence, IJCAI 2001, Seattle, Washington, USA, August 4-10, 2001, edited by B. Nebel, Morgan Kaufmann (2001) 309–315.
G. Dooms, Y. Deville and P. Dupont, CP(Graph): Introducing a Graph Computation Domain in Constraint Programming, in Principles and Practice of Constraint Programming (CP'2005), edited by P. van Beek, Springer-Verlag, Lect. Notes Comput. Sci. 3709 (2005) 211–225.
Freuder, E.C. and Wallace, R.J., Partial constraint satisfaction. Artificial Intelligence 58 (1992) 21–70. CrossRef
M.R. Garey and D.S. Johnson, Computers and intractability: A guide to the theory of NP-completeness. W.H. Freeman and Company (1979).
Hanák, D., Implementing Global Constraints as Structured Graphs of Elementary Constraints. Scientific Journal Acta Cybernetica 16 (2003) 241–258.
Van Hentenryck, P., Deville, Y. and Teng, C.M., Generic Arc Consistency Al, Agorithm and its Specializations. Artificial Intelligence 57 (1992) 291–321. CrossRef
Van Hentenryck, P., Saraswat, V. and Deville, Y., Design, implementation, and evaluation of the constraint language cc(FD). J. Logic Programming 37 (1998) 139–164. CrossRef
I. Katriel and S. Thiel, Fast Bound Consistency for the global cardinality Constraint, in Principles and Practice of Constraint Programming (CP'2003), edited by F. Rossi, Springer-Verlag, Lect. Notes Comput. Sci. 2833 (2003) 437–451. CrossRef
K. Mehlhorn and S. Thiel, Faster Algorithms for Bound-Consistency of the sortedness and the alldifferent Constraint, in Principles and Practice of Constraint Programming (CP'2000), edited by R. Dechter, Springer-Verlag, Lect. Notes Comput. Sci. 1894 (2000) 306–319. CrossRef
Montanari, U., Networks of constraints: Fundamental properties and applications to picture processing. Information Science 7 (1974) 95–132. CrossRef
Norman, R.Z. and Rabin, M.O., An algorithm for minimum cover of a graph. American Math. Soc. 10 (1959) 315–319. CrossRef
G. Pesant, A Regular Language Membership Constraint for Finite Sequences of Variables, in Principles and Practice of Constraint Programming (CP'2004) edited by M. Wallace, Springer-Verlag, Lect. Notes Comput. Sci. 3258 (2004) 482–495. CrossRef
T. Petit, J-C. Régin and C. Bessière, Meta constraints on violations for over constrained problems, in 12th IEEE International Conference on Tools with Artificial Intelligence (ICTAI 2000), 13-15 November 2000, Vancouver, BC, Canada, IEEE Computer Society (2000) 358–365.
T. Petit, J-C. Régin and C. Bessière, Specific filtering algorithms for over constrained problems, in Principles and Practice of Constraint Programming (CP'2001), edited by T. Walsh, Springer-Verlag, Lect. Notes Comput. Sci. 2239 (2001) 451–463. CrossRef
C.-G. Quimper, A. López-Ortiz, P. van Beek and A. Golynski, Improved Algorithms for the global cardinality Constraint, in Principles and Practice of Constraint Programming (CP'2004), edited by M. Wallace, Springer-Verlag, Lect. Notes Comput. Sci. 3258 (2004) 542–556.
J.-C. Régin, A Filtering Algorithm for Constraints of Difference in CSP, in 12th National Conference on Artificial Intelligence (AAAI-94) (1994) 362–367.
J.-C. Régin, Generalized Arc Consistency for global cardinality Constraint, in 14th National Conference on Artificial Intelligence (AAAI-96) (1996) 209–215.
J.-C. Régin, The Symmetric alldiff Constraint, in 16th Int. Joint Conf. on Artificial Intelligence (IJCAI-99) (1999) 420–425.
Turán, P., On an Extremal Problem in Graph Theory. Mat. Fiz. Lapok 48 (1941) 436–452, in Hungarian.
W.-J. van Hoeve, A Hyper-Arc Consistency Algorithm for the soft alldifferent Constraint, in Principles and Practice of Constraint Programming (CP'2004), edited by M. Wallace, Springer-Verlag, Lect. Notes Comput. Sci. 3258 (2004) 679–689.
W.-J. van Hoeve, G. Pesant and L.-M. Rousseau, On global warming: Flow-based soft global constraints, in Journal of Heuristics 12 (2006) 347–373.
N.R. Vempaty, Solving Constraint Satisfaction Problems using Finite State Automata, in National Conference on Artificial Intelligence (AAAI-92), AAAI Press (1992) 453–458.