Finding the shortest path on uncertain transportation networks is a great challenge in theory and practice. There are several resources of uncertainty in the transportation networks such as traffic congestion, weather conditions, vehicle accidents, repairing roads, etc. A natural way to model uncertain networks is utilizing graphs with uncertain edges, that is, the weight of each edge, as the traveling time, may vary in an interval. In this paper, we not only discuss the theoretical aspect of this issue, but also propose a practical approach to find the shortest path on uncertain graphs. The approach has two phases; a preprocessing phase and a query phase. In the preprocessing phase, we construct a general map that contains all the edges that may lie on some shortest path, and in the query phase, when the weights are determined certainly, we find the shortest path using the map. Finally, we demonstrate the effectiveness of the proposed algorithm on both random generated graphs and real-world networks. Also, we compare it with other shortest path algorithms in the uncertainty context and shows its efficiency.

在不确定的运输网络上寻找最短路径是理论和实践中的巨大挑战。交通网络中存在多种不确定性资源，例如交通拥堵，天气状况，车辆事故，修路等。对不确定性网络建模的自然方法是利用具有不确定边缘的图，即每个边缘的权重，如行驶时间可能会有所间隔。在本文中，我们不仅讨论了该问题的理论方面，而且提出了一种实用的方法来找到不确定图上的最短路径。该方法分为两个阶段。一个预处理阶段和查询阶段。在预处理阶段，我们构建一个包含所有可能位于某个最短路径上的所有边的通用地图，而在查询阶段，当确定权重时，我们会使用该地图找到最短路径。最后，我们在随机生成的图和真实世界的网络上证明了该算法的有效性。此外，我们在不确定性上下文中将其与其他最短路径算法进行了比较，并显示了其效率。