Optimal path query based on cost function over multi-cost graphs

Graphs have been widely used to model complex relationships among various entities in real applications. Shortest path query is an important problem in graphs and has been well-studied. However, most approaches for shortest path are based on single-cost (weight) graphs. However, it is non-sufficient that considering only one cost type. In this paper, we introduce the definition of multi-cost graph and propose a new query: the optimal path query based on function over multi-cost graphs. Most existing methods to compute shortest path utilize the property of optimal sub-path in shortest path: any sub-path of a shortest path is also a shortest path. Thus, they only need to maintain the shortest path from starting node to any visited node (not ending node) when computing shortest path. Unfortunately, the optimal sub-path property doesn't hold in multi-cost graphs. We propose a best-first search branch and bound algorithm and three optimizing strategies. We also propose a vertex-filtering algorithm to filter a large proportion of vertices from graph. We confirmed the effectiveness and efficiency of our algorithms using real-life datasets in experiments.