Best-first search methods for constrained two-dimensional cutting stock problems
Operations Research
Exact algorithms for the guillotine strip cutting/packing problem
Computers and Operations Research
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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
An Exact Approach to the Strip-Packing Problem
INFORMS Journal on Computing
A Combinatorial Characterization of Higher-Dimensional Orthogonal Packing
Mathematics of Operations Research
Computers and Operations Research
A new constraint programming approach for the orthogonal packing problem
Computers and Operations Research
An Exact Algorithm for Higher-Dimensional Orthogonal Packing
Operations Research
Generating optimal two-section cutting patterns for rectangular blanks
Computers and Operations Research
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
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We consider the problem of determining whether a given set of rectangular items can be cut from a larger rectangle using so-called guillotine cuts only. We introduce a new class of arc-colored directed graphs called guillotine graphs and show that each guillotine graph can be associated with a specific class of pattern solutions that we call a guillotine-cutting class. The properties of guillotine graphs are examined, and some effective algorithms for dealing with guillotine graphs are proposed. As an application, we then describe a constraint programming method based on guillotine graphs, and we propose effective filtering techniques that use the graph model properties in order to reduce the search space efficiently. Computational experiments are reported on benchmarks from the literature: our algorithm outperforms previous methods when solving the most difficult instances exactly.