Any set function can be decomposed into the difference of two monotone nondecreasing submodular functions. This theorem plays an important role in the set function optimization theory. In this paper, we show a variation that any set function can be decomposed into the difference of two monotone nondecreasing supermodular functions. Meanwhile, we give an example in social network optimization and construct algorithmic solutions for the maximization problem of set functions with this variation of DS decomposition.

中文翻译：

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集函数优化中DS分解的变化

任何集合函数都可以分解为两个单调非递减子模函数的差。该定理在集合函数优化理论中起着重要作用。在本文中，我们展示了一种变体，即任何集合函数都可以分解为两个单调非递减超模函数的差。同时，我们给出了一个社会网络优化示例，并构造了具有这种DS分解变化的集合函数最大化问题的算法解决方案。