Finding the Shortest Path with Vertex Constraint over Large Graphs

Graph is an important complex network model to describe the relationship among various entities in real applications, including knowledge graph, social network, and traffic network. Shortest path query is an important problem over graphs and has been well studied. This paper studies a special case of the shortest path problem to find the shortest path passing through a set of vertices specified by user, which is NP-hard. Most existing methods calculate all permutations for given vertices and then find the shortest one from these permutations. However, the computational cost is extremely expensive when the size of graph or given set of vertices is large. In this paper, we first propose a novel exact heuristic algorithm in best-first search way and then give two optimizing techniques to improve efficiency. Moreover, we propose an approximate heuristic algorithm in polynomial time for this problem over large graphs. We prove the ratio bound is 3 for our approximate algorithm. We confirm the efficiency of our algorithms by extensive experiments on real-life datasets. The experimental results validate that our algorithms always outperform the existing methods even though the size of graph or given set of vertices is large.