Abstract
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.
Highlights
Graph is an important complex network model to describe the relationship among various entities in real applications, including knowledge graph, RDF graph, linked data, social network, biological network, and traffic network [1,2,3,4]
In knowledge graphs, it is to find the closest connection between two entities or concepts; in social networks, it is to find the closest relationships such as friendship between two individuals; in traffic networks, it is to compute the shortest route between two locations
(ii) We propose an approximate algorithm in polynomial time for our problem over large graphs
Summary
Graph is an important complex network model to describe the relationship among various entities in real applications, including knowledge graph, RDF graph, linked data, social network, biological network, and traffic network [1,2,3,4]. Shortest path query is a basic problem on graph model. In knowledge graphs, it is to find the closest connection between two entities or concepts; in social networks, it is to find the closest relationships such as friendship between two individuals; in traffic networks, it is to compute the shortest route between two locations. A critical problem is how to find a route with the minimum length passing through these locations. In above examples, both knowledge graph and traffic network can be modeled as a large graph G(V, E). The subset Vs is called vertex constraint; that is, the shortest path must pass through every vertex in the subset Vs
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