Top-k Critical Vertices Query on Shortest Path

        Shortest path query is one of the most fundamental and classic problems in graph analytics, which returns the complete shortest path between any two vertices. However, in many real-life scenarios, only critical vertices on the shortest path are desirable and it is unnecessary to search for the complete path. This paper investigates the shortest path sketch by defining a top-k critical vertices ($k$CV) query on the shortest path. Given a source vertex s and target vertex t in a graph, $k$CV query can return the top-k significant vertices on the shortest path SP($s,t$). The significance of the vertices can be predefined. The key strategy for seeking the sketch is to apply off-line preprocessed distance oracle to accelerate on-line real-time queries. This allows to omit unnecessary vertices and obtain the most representative sketch of the shortest path directly. We further explore a series of methods and optimizations to answer $k$CV query on both centralized and distributed platforms, using exact and approximate approaches, respectively. We evaluate our methods in terms of time, space complexity and approximation quality. Experiments on large-scale real networks validate that our algorithms are of high efficiency and accuracy.