We consider a time‐dependent shortest path problem with possible waiting at some nodes of the graph and a global bound W on the total waiting time. The goal is to minimize the time traveled along the edges of the path, not including the waiting time. We prove that the problem can be solved in polynomial time when the travel time functions are piecewise linear and continuous. The algorithm relies on a recurrence relation characterized by a bound ω on the total waiting time, where 0 ≤ ω ≤ W. We show that only a small number of values ω1, ω2, …, ωK need to be considered, where K depends on the total number of breakpoints of all travel time functions.

中文翻译：

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在具有等待的一致时间相关网络中最小化旅行时间的多项式算法

我们考虑一个时间相关的最短路径问题，可能在图的某些节点等待，并且总等待时间有一个全局边界 W。目标是最小化沿路径边缘行进的时间，不包括等待时间。我们证明了当走时函数是分段线性和连续的时，该问题可以在多项式时间内解决。该算法依赖于以总等待时间上界 ω 为特征的递推关系，其中 0 ≤ ω ≤ W。我们表明只需要考虑少量值 ω1、ω2、...、ωK，其中 K 取决于所有旅行时间函数的断点总数。