Shortest path problem on uncertain networks: An efficient two phases approach

Abstract

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.