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Which rectangle sets have perfect packings?

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  • Braam, Florian
  • van den Berg, Daan

Abstract

In the perfect rectangle packing problem, a set of rectangular items have to be placed inside a rectangular container without overlap or empty space. In this paper, we generate a large number of random instances and decide them all with an exact solving algorithm. Both an instance’s solution probability and its hardness measured in recursions or system time, seems to critically depend on tmax, a parameter in the generation procedure that assigns the maximally choosable random side lengths of items in the instance. We numerically characterize the solvability across instance sizes, and derive a rule for generating (un)solvable problem instances of arbitrary size.

Suggested Citation

  • Braam, Florian & van den Berg, Daan, 2022. "Which rectangle sets have perfect packings?," Operations Research Perspectives, Elsevier, vol. 9(C).
    • Handle: RePEc:eee:oprepe:v:9:y:2022:i:c:s2214716021000270
    DOI: 10.1016/j.orp.2021.100211
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    References listed on IDEAS

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