Public transport administrators rely on efficient algorithms for various problems that arise in public transport networks. In particular, our study focused on designing linear-time algorithms for two fundamental path problems: the earliest arrival time (\textsc{eat}) and the fastest path duration (\textsc{fpd}) on public transportation data. We conduct a comparative analysis with state-of-the-art algorithms. The results are quite promising, indicating substantial efficiency improvements. Specifically, the fastest path problem shows a remarkable 34-fold speedup, while the earliest arrival time problem exhibits an even more impressive 183-fold speedup. These findings highlight the effectiveness of our algorithms to solve \textsc{eat} and \textsc{fpd} problems in public transport, and eventually help public administrators to enrich the urban transport experience.

翻译：公共交通管理者依赖于高效算法来解决公共交通网络中出现的各类问题。本研究聚焦于为两个基础路径问题设计线性时间算法：公共交通数据上的最早到达时间（\textsc{eat}）与最快路径持续时间（\textsc{fpd}）。我们与当前最优算法进行了比较分析，结果令人振奋，显示出显著的效率提升。具体而言，最快路径问题实现了34倍的加速，而最早到达时间问题更展现出惊人的183倍加速效果。这些发现凸显了我们的算法在解决公共交通中\textsc{eat}与\textsc{fpd}问题的有效性，并最终有助于公共管理者优化城市交通体验。