Sweep as a Generic Pruning Technique Applied to the Non-overlapping Rectangles Constraint
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Non-overlapping Constraints between Convex Polytopes
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Constraint-driven floorplan repair
Proceedings of the 43rd annual Design Automation Conference
ECO-system: Embracing the Change in Placement
ASP-DAC '07 Proceedings of the 2007 Asia and South Pacific Design Automation Conference
Search Strategies for Rectangle Packing
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
New improvements in optimal rectangle packing
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
New filtering for the cumulative constraint in the context of non-overlapping rectangles
CPAIOR'08 Proceedings of the 5th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
A generic visualization platform for CP
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
Weibull-Based benchmarks for bin packing
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
Optimal rectangle packing: an absolute placement approach
Journal of Artificial Intelligence Research
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The almost square rectangle packing problem involves packing all rectangles with sizes 1×2 to n×(n+1) (almost squares) into an enclosing rectangle of minimal area. This extends the previously studied square packing problem by adding an additional degree of freedom for each rectangle, deciding in which orientation the item should be packed. We show how to extend the model and search strategy that worked well for square packing to solve the new problem. Some adapted versions of known redundant constraints improve overall search times. Based on a visualization of the search tree, we derive a decomposition method that initially only looks at the subproblem given by one of the cumulative constraints. This decomposition leads to further modest improvements in execution times. We find a solution for problem size 26 for the first time and dramatically improve best known times for finding solutions for smaller problem sizes by up to three orders of magnitude.