In this paper, we consider the k-sink location problem in a path network with the goal of optimizing a combinational function of the maximum completion time and the total completion time. Let \(P=\left( V,E\right) \) be an undirected path network with n vertices. Each vertex has a positive weight, indicating the initial amount of supplies, and each edge has a positive length and a uniform capacity, which is the maximum amount of supplies that can enter the edge per unit time. Our goal is to identify k sink locations on the path P so that all supplies will be successfully evacuated and the given objective function is optimized. This paper presents two efficient polynomial time algorithms, which achieve \(O\left( n \right) \) for \(k=1\) and \(O\left( n^6 \right) \) for general k, respectively.

在本文中，我们考虑路径网络中的k汇点定位问题，以优化最大完成时间和总完成时间的组合函数为目标。令\（P = \ left（V，E \ right）\）是具有n个顶点的无向路径网络。每个顶点的权重为正，表示初始供应量，每个边缘的长度为正，容量均匀，这是每单位时间可以进入边缘的最大供应量。我们的目标是确定路径P上的k个汇点位置，以便成功撤离所有电源并优化给定的目标函数。本文提出了两种有效的多项式时间算法，它们可以实现\（O \左侧（N \右）\）为\（K = 1 \）和（O \左侧（N ^ 6 \右）\）\一般ķ，分别。