Abstract
The geost constraint has been proposed to model and solve discrete placement problems involving multi-dimensional boxes (packing in space and time). The filtering technique is based on a sweeping algorithm that requires the ability for each constraint to compute a forbidden box around a given fixed point and within a surrounding area. Several cases have been studied so far, including integer linear inequalities. Motivated by the placement of objects with curved shapes, this paper shows how to implement this service for continuous constraints with arbitrary mathematical expressions. The approach relies on symbolic processing and defines a new interval arithmetic.
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References
Choco: An open source Java CP library. documentation, http://choco.emn.fr/ .
Agren, M., Beldiceanu, N., Carlsson, M., Sbihi, M., Tuchet, C., Zampelli, S.: 6 Ways of Integreting Symmetries Within Non-Overlapping Constraints. In: van Hoeve, W.-J., Hooker, J.N. (eds.) CPAIOR 2009. LNCS, vol. 5547, pp. 11–25. Springer, Heidelberg (2009)
Araya, I., Trombettoni, G., Neveu, B.: Filtering Numerical CSPs Using Well-Constrained Subsystems. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 158–172. Springer, Heidelberg (2009)
Beldiceanu, N., Carlsson, M.: Sweep as a Generic Pruning Technique Applied to the Non-Overlapping Rectangles Constraints. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 377–391. Springer, Heidelberg (2001)
Beldiceanu, N., Carlsson, M., Poder, E., Sadek, R., Truchet, C.: A Generic Geometrical Constraint Kernel in Space and Time for Handling Polymorphic k-Dimensional Objects. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 180–194. Springer, Heidelberg (2007)
Beldiceanu, N., Carlsson, M., Thiel, S.: Sweep Synchronisation as a Global Propagation Mechanism. Comp. & Operations Research 33(10), 2835–2851 (2006)
Benhamou, F., Goualard, F., Granvilliers, L., Puget, J.-F.: Revising Hull and Box Consistency. In: ICLP, pp. 230–244 (1999)
Carlsson, M., Beldiceanu, N., Martin, J.: A Geometric Constraint over k-Dimensional Objects and Shapes Subject to Business Rules. In: Stuckey, P.J. (ed.) CP 2008. LNCS, vol. 5202, pp. 220–234. Springer, Heidelberg (2008)
Carlsson, M., Ottosson, G., Carlson, B.: An open-ended finite domain constraint solver. In: 9th International Symposium on Programming Languages: Implementations, Logics, and Programs, vol. 1292, pp. 191–206 (1997)
Kuchcinski, K.: Constraints-driven scheduling and resource assignment. ACM Transactions on Design Automation of Electronic Systems 8(3), 355–383 (2003)
Mackworth, A.K.: Consistency in Networks of Relations. Artificial Intelligence 8, 99–118 (1977)
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Chabert, G., Beldiceanu, N. (2010). Sweeping with Continuous Domains. In: Cohen, D. (eds) Principles and Practice of Constraint Programming – CP 2010. CP 2010. Lecture Notes in Computer Science, vol 6308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15396-9_14
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DOI: https://doi.org/10.1007/978-3-642-15396-9_14
Publisher Name: Springer, Berlin, Heidelberg
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