In this research, we examine the minsum flow problem in dynamic path networks where flows are represented as discrete and weighted sets. The minsum flow problem has been widely studied for its relevance in finding evacuation routes during emergencies such as earthquakes. However, previous approaches often assume that individuals are separable and identical, which does not adequately account for the fact that some groups of people, such as families, need to move together and that some groups may be more important than others. To address these limitations, we modify the minsum flow problem to support flows represented as discrete and weighted sets. We also propose a 2-approximation pseudo-polynomial time algorithm to solve this modified problem for path networks with uniform capacity.

翻译：本研究探讨了动态路径网络中的最小和流问题，其中流被表示为离散且加权的集合。最小和流问题因其在紧急情况（如地震）下寻找疏散路径的相关性而得到广泛研究。然而，先前的方法通常假设个体是可分离且同质的，这未能充分考虑某些人群（如家庭）需要共同移动，以及某些群体可能比其他群体更重要的事实。为应对这些局限，我们修改了最小和流问题，以支持表示为离散加权集合的流。此外，针对具有均匀容量的路径网络，我们提出了一种2-近似伪多项式时间算法来解决这一修改后的问题。