Shortest path tree sampling for landmark selection in large networks

Abstract Computing the distance between vertices in a large dynamic network is an important task in many real-time applications. An exact real-time computation is often infeasible, due to the network size, dynamic changes and the requirement for rapid response. We hence revert to estimates. One popular method for distance estimation uses a set of vertices, called landmarks, whose distance from all other vertices is computed offline. Then, the online query estimates the distance between two arbitrary vertices by summing the computed distances from the source to a landmark and from the landmark to the target. In this paper we suggest a new method for computing the set of landmarks, based on a sampled set of shortest path trees (SPTs). The SPTs provide a good estimation of the number of shortest paths that a vertex covers, which is strongly correlated with distance estimation error. We provide an extensive set of experiments, comparing the proposed Sampled SPTs method to state of the art, and show that our approach provides lower distance estimation errors on a wide set of benchmarks. We further analyse the time and space complexities of our method, and its sensitivity to the number of the sampled SPTs, as well as the number of landmarks, showing our method to consistently outperforms other approaches.