Fast top-k simple shortest paths discovery in graphs

• Authors: Jun Gao;Huida Qiu;Xiao Jiang;Tengjiao Wang;Dongqing Yang
• Venue: CIKM '10 Proceedings of the 19th ACM international conference on Information and knowledge management
• Year: 2010

With the wide applications of large scale graph data such as social networks, the problem of finding the top-k shortest paths attracts increasing attention. This paper focuses on the discovery of the top-k simple shortest paths (paths without loops). The well known algorithm for this problem is due to Yen, and the provided worstcase bound O(kn(m + nlogn)), which comes from O(n) times single-source shortest path discovery for each of k shortest paths, remains unbeaten for 30 years, where n is the number of nodes and m is the number of edges. In this paper, we observe that there are shared sub-paths among O(kn) single-source shortest paths. The basic idea behind our method is to pre-compute the shortest paths to the target node, and utilize them to reduce the discovery cost at running time. Specifically, we transform the original graph by encoding the pre-computed paths, and prove that the shortest path discovered over the transformed graph is equivalent to that in the original graph. Most importantly, the path discovery over the transformed graph can be terminated much earlier than before. In addition, two optimization strategies are presented. One is to reduce the total iteration times for shortest path discovery, and the other is to prune the search space in each iteration with an adaptively-determined threshold. Although the worst-case complexity cannot be lowered, our method is proven to be much more efficient in a general case. The final extensive experimental results (on both real and synthetic graphs) also show that our method offers a significant performance improvement over the existing ones.