Optimal Rectangle Packing: A Meta-CSP Approach

Michael D. Moffitt, Martha E. Pollack

We present a new approach to optimal rectangle packing, an NP-complete problem that can be used to model many simple scheduling tasks. Recent attempts at incorporating artificial intelligence search techniques to the problem of rectangle packing have focused on a CSP formulation, in which partial assignments are defined to be the fixed placement of a subset of rectangles. Our technique takes a significant departure from this search space, as we instead view partial assignments as subsets of relative pairwise relationships between rectangles. This approach recalls the meta-CSP commonly constructed in constraint-based temporal reasoning, and is thus a candidate for several pruning techniques that have been developed in that field. We apply these to the domain of rectangle packing, and develop a suite of new techniques that exploit both the symmetry and geometry present in this particular domain. We then provide experimental results demonstrating that our approach performs competitively compared to the previous state-of-the-art on a series of benchmarks, matching or surpassing it in speed on nearly all instances. Finally, we conjecture that our technique is particularly appropriate for problems containing large rectangles, which are difficult for the fixed-placement formulation to handle efficiently.

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