Efficiently Computing Top-K Shortest Path Join

Driven by many applications, in this paper we study the problem of computing the top-k shortest paths from one set of target nodes to another set of target nodes in a graph, namely the top-k shortest path join (KPJ) between two sets of target nodes. While KPJ is an extension of the problem of computing the top-k shortest paths (KSP) between two target nodes, the existing technique by converting KPJ to KSP has several deficiencies in conducting the computation. To resolve these, we propose to use the best-first paradigm to recursively divide search subspaces into smaller subspaces, and to compute the shortest path in each of the subspaces in a prioritized order based on their lower bounds. Consequently, we only compute shortest paths in subspaces whose lower bounds are larger than the length of the current k-th shortest path. To improve the efficiency, we further propose an iteratively bounding approach to tightening lower bounds of subspaces. Moreover, we propose two index structures which can be used to reduce the exploration area of a graph dramatically; these greatly speed up the computation. Extensive performance studies based on real road networks demonstrate the scalability of our approaches and that our approaches outperform the existing approach by several orders of magnitude. Furthermore, our approaches can be immediately used to compute KSP. Our experiment also demonstrates that our techniques outperform the state-of-the-art algorithm for KSP by several orders of magnitude.