Abstract
Constraint Programming (CP) has been successfully applied to numerous combinatorial problems such as scheduling, graph coloring, circuit analysis, or DNA sequencing. Following the success of CP over traditional domains, set variables were also introduced to more declaratively solve a number of different problems.
Using a bounds representation for a finite set variable allows one to compactly represent the solution set of a set constraint problem. Many consistency mechanisms for maintaining bounds consistency have been proposed and in this paper we propose to use delta domain variable information to speed up constraint propagation. Additionally, we propose the use of indexed set domain variable representations as a better means of improving the use, intuitiveness and efficiency of delta domain variables for propagation tasks.
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References
Gervet, C.: Interval Propagation to Reason about Sets: Definition and Implementation of a Practical Language. Constraints journal 1(3), 191–244 (1997)
Azevedo, F.: Cardinal: A finite sets constraint solver. Constraints journal 12(1), 93–129 (2007)
ECLiPSE Constraint System, http://eclipse.crosscoreop.com/
Correia, M., Barahona, P., Azevedo, F.: Casper: A programming environment for development and integration of constraint solvers. In: Azevedo, F., Gervet, C., Pontelli, E. (eds.) Proceedings of the First International Workshop on Constraint Programming Beyond Finite Integer Domains (BeyondFD 2005), pp. 59–73 (2005)
CaSPER: Constraint Solving Programming Environment for Research, http://proteina.di.fct.unl.pt/casper/
Azevedo, F.: Constraint Solving over Multi-Valued Logics. Frontiers in Artificial Intelligence and Applications, vol. 91. IOS Press, Amsterdam (2003)
Lagerkvist, M., Schulte, C.: Advisors for incremental propagation. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 409–422. Springer, Heidelberg (2007)
Viegas, R.D., Azevedo, F.: GRASPER: A Framework for Graph CSPs. In: Lee, J., Stuckey, P. (eds.) Proceedings of the Sixth International Workshop on Constraint Modelling and Reformulation (ModRef 2007), Providence, Rhode Island, USA (September 2007)
Viegas, R.D., Azevedo, F.: GRASPER: A Framework for Graph Constraint Satisfaction Problems. In: Analide, C., Novais, P., Henriques, P. (eds.) Simpósio Doutoral em Inteligência Artificial, Guimarães, Portugal (December 2007)
Viegas, R.D., Azevedo, F.: GRASPER: A Framework for Graph Constraint Satisfaction Problems. In: Azevedo, F., Lynce, I., Manquinho, V. (eds.) Search Techniques for Constraint Satisfaction, Guimarães, Portugal (December 2007)
Viegas, R.D.: Constraint Solving over Finite Graphs. Master’s thesis, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa (2008)
Padberg, M.W.: Covering, Packing and Knapsack Problems. Annals of Discrete Mathematics, vol. 4 (1979)
Beasley, J.: An algorithm for set covering problems. European Journal of Operational Research 31, 85–93 (1987)
Cormen, T., Leiserson, C., Rivest, R., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001)
Beasley, J.: A Lagrangian Heuristic for Set-Covering problems. Naval Research Logistics (NRL) 37(1), 151–164 (1990)
Mathews, C., van Holde, K.: Biochemistry, 2nd edn. Benjamin Cummings (1996)
Attwood, T., Parry-Smith, D.: Introduction to Bioinformatics. Prentice-Hall, Englewood Cliffs (1999)
Sellmann, M.: Cost-based filtering for shorter path constraints. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 694–708. Springer, Heidelberg (2003)
Dooms, G.: The CP(Graph) Computation Domain in Constraint Programming. PhD thesis, Faculté des Sciences Appliquées, Université Catholique de Louvain (2006)
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Viegas, R.D., Correia, M., Barahona, P., Azevedo, F. (2008). Using Indexed Finite Set Variables for Set Bounds Propagation. In: Geffner, H., Prada, R., Machado Alexandre, I., David, N. (eds) Advances in Artificial Intelligence – IBERAMIA 2008. IBERAMIA 2008. Lecture Notes in Computer Science(), vol 5290. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88309-8_8
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DOI: https://doi.org/10.1007/978-3-540-88309-8_8
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