哪些矩形集合有完美的包装?

IF 3.7 4区管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Operations Research Perspectives Pub Date : 2022-01-01 DOI:10.1016/j.orp.2021.100211

Florian Braam , Daan van den Berg

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引用次数: 5

摘要

在完美矩形包装问题中，一组矩形物品必须放置在一个矩形容器中，没有重叠或空白空间。在本文中，我们生成了大量的随机实例，并用一种精确求解算法来确定它们。实例的解决概率和它在递归或系统时间中测量的硬度似乎都严重依赖于tmax, tmax是生成过程中的一个参数，用于分配实例中项目的最大可选随机边长度。我们在数值上描述了跨实例大小的可解性，并推导了生成任意大小的(不可)可解问题实例的规则。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Which rectangle sets have perfect packings?

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 $t_{m a x}$ , 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.

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