灌装桶与同等尺寸 [英] Filling bins with an equal size

问题描述

我有100组，每组有里面的一些元素。对于交叉验证，我想提出五个组，他们的尺寸尽可能相等。

I have 100 groups and each group has some elements inside. For the cross validation, I want to make five bins which their size is as equal as possible.

有什么算法用于此目的。

Is there any algorithm for this purpose.

5组和2箱一个例子：

An example for 5 groups and 2 bins:

Group_1: 5
Group_2: 6
Group_3: 2
Group_4: 7
Group_5: 1

这两个桶将是：

The two bins will be:

G1和G2 - >他们的总和等于11

G1 and G2 -> their sum is equal to 11.

G3，G4和G5。 - >他们的总和等于10

G3, G4 and G5 -> their sum is equal to 10.

推荐答案

这似乎涉及到设置划分问题，这是 NP -hard幸好承认很多很好的近似算法和伪多项式时间动态规划算法。你可能想看看那些为出发点，因为有已经相当大量的工作是在这方面开展的工作。

This seems related to the set partitioning problem, which is NP-hard but fortunately admits lots of good approximation algorithms and pseudopolynomial-time dynamic programming algorithms. You may want to look into those as a starting point, since there's already quite a lot of work that's been done in this area.

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