In this paper, we propose new algorithms for evacuation problems defined on dynamic flow networks. A dynamic flow network is a directed graph in which source nodes are given supplies and a single sink node is given a demand. The evacuation problem seeks a dynamic flow that sends all supplies from sources to the sink such that its demand is satisfied in the minimum feasible time horizon. For this problem, the current best algorithms are developed by Schlöter (2018) and Kamiyama (2019), which run in strongly polynomial time but with high-order polynomial time complexity because they use submodular function minimization as a subroutine. In this paper, we propose new algorithms that do not explicitly execute submodular function minimization, and we prove that they are faster than the current best algorithms when an input network is restricted such that the sink has a small in-degree and every edge has the same capacity.

在本文中，我们提出了针对动态流网络上定义的疏散问题的新算法。动态流网络是一个有向图，其中源节点被给予供应，而单个汇节点被给予需求。疏散问题寻求一种动态流，将所有供给从源发送到接收器，以便在最小可行时间范围内满足其需求。对于这个问题，目前最好的算法是由 Schlöter (2018) 和 Kamiyama (2019) 开发的，它们在强多项式时间内运行，但具有高阶多项式时间复杂度，因为它们使用子模函数最小化作为子程序。在本文中，我们提出了不显式执行子模函数最小化的新算法，并且证明当输入网络受到限制使得汇具有较小的入度并且每条边具有相同的容量。