A new graph-theoretical model for k-dimensional guillotine-cutting problems

Authors:
François Clautiaux;Antoine Jouglet;Aziz Moukrim
Affiliations:
Université des Sciences et Technologies de Lille, LIFL, UMR, CNRS, Bâtiment INRIA, Villeneuve d'Ascq;HeuDiaSyC UMR, CNRS, UTC, Compiègne;HeuDiaSyC UMR, CNRS, UTC, Compiègne
Venue:
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
Year:
2008

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Abstract

We consider the problem of determining if a given set of rectangular items can be cut in a large rectangle, using guillotine cuts only. We introduce a new class of arc-colored and oriented graphs, named guillotine graphs, which model guillotine patterns. Then we show that an uncolored and non-oriented multigraph is sufficient to obtain any guillotine pattern. We propose linear algorithms for recognizing these graphs, and computing the corresponding patterns. Finally we explain how the model can be used in a constraint programming approach.