We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and requires exponential complexity to solve (i.e., intractable); we formulate a weaker version of this NP-hard problem, where the goal is to find a locally optimal solution. We show that our proposed algorithms can find a locally optimal solution in near linear time. Our algorithms require neither positive nor integer elements in the input set, hence, they are more widely applicable.

翻译：我们研究设定分区问题的优化版本(在最小化分区总和差异的情况下),这在决定理论文献中有许多应用。设定的分区问题虽然是NP硬的,需要指数复杂性才能解决(即难以解决);我们对这个NP硬问题设计了一个较弱的版本,目的是找到一个本地最佳解决方案。我们显示,我们提议的算法可以在近线性时间内找到一个本地最佳解决方案。我们的算法不需要输入集中的正或整数元素,因此,它们的适用范围更广。