We consider a Two-Bar Charts Packing Problem (2-BCPP), in which it is necessary to pack two-bar charts (2-BCs) in a unit-height strip of minimum length. The problem is a generalization of the Bin Packing Problem (BPP). Earlier, we proposed an $O(n^2)$-time algorithm that constructs the packing which length at most $2\cdot OPT+1$, where $OPT$ is the minimum length of the packing of $n$ 2-BCs. In this paper, we propose an $O(n^4)$-time 3/2-approximate algorithm when each BC has at least one bar greater than 1/2.

中文翻译：

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一个 3/2-- 大两柱形图包装的近似值

我们考虑一个双条形图打包问题 (2-BCPP)，其中有必要将两个条形图 (2-BC) 打包在最小长度的单位高度条带中。该问题是装箱问题 (BPP) 的泛化。早些时候，我们提出了一个$O(n^2)$-time 算法，该算法构造长度最多为$2\cdot OPT+1$ 的包装，其中$OPT$ 是$n$ 2-BCs 的包装的最小长度. 在本文中，当每个 BC 至少有一个大于 1/2 的柱时，我们提出了一种 $O(n^4)$-time 3/2-approximate 算法。