A Generic Geometrical Constraint Kernel in Space and Time for Handling Polymorphic k-Dimensional Objects
This paper introduces a geometrical constraint kernel for handling the location in space and time of polymorphic k-dimensional objects subject to various geometrical and time constraints. The constraint kernel is generic in the sense that one of its parameters is a set of constraints on subsets of the objects. These constraints are handled globally by the kernel.
We first illustrate how to model several placement problems with the constraint kernel. We then explain how new constraints can be introduced and plugged into the kernel. Based on these interfaces, we develop a generic k-dimensional lexicographic sweep algorithm for filtering the attributes of an object (i.e., its shape and the coordinates of its origin as well as its start, duration and end in time) according to all constraints where the object occurs. Experiments involving up to hundreds of thousands of objects and 1 million integer variables are provided in 2, 3 and 4 dimensions, both for simple shapes (i.e., rectangles, parallelepipeds) and for more complex shapes.
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- 4.Clautiaux, F., Jouglet, A., Carlier, J., Moukrim, A.: A new constraint programming approach for the orthogonal packing problem. Computers and Operation Research (to appear)Google Scholar
- 5.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. SICS Technical Report T2007:08, Swedish Institute of Computer Science (2007)Google Scholar
- 6.Van Hentenryck, P.: Scheduling and packing in the constraint language cc(FD). In: Zweben, M., Fox, M. (eds.) Intelligent Scheduling, Morgan Kaufmann, San Francisco (1994)Google Scholar
- 7.Colmerauer, A., Gilleta, B.: Solving the three-dimensional pentamino puzzle. Technical report, Laboratoire d’Informatique de Marseille (1999), http://www.lim.univ-mrs.fr/~colmer/ArchivesPublications/Giletta/misc99.pdf
- 8.Bouwkamp, C.J., Duijvestijn, A.J.W.: Catalogue of simple perfect squared squares of orders 21 through 25. Technical Report EUT Report 92-WSK-03, Eindhoven University of Technology, The Netherlands (November 1992)Google Scholar
- 9.Clautiaux, F., Carlier, J., Moukrim, A.: A new exact method for the two-dimensional orthogonal packing problem. European Journal of Operational Research (to appear)Google Scholar
- 10.Van Hentenryck, P., Saraswat, V., Deville, Y.: Constraint processing in cc(FD). Manuscript (1991)Google Scholar
- 11.Sidebottom, G.: A Language for Optimizing Constraint Propagation. PhD thesis, Simon Fraser University (1993)Google Scholar