HD-GDD: High Dimensional Graph Dominance Drawing Approach for Reachability Query

Efficiently answering reachability queries, which checks whether one vertex can reach another in a directed graph, has been studied extensively during recent years. However, the size of the graph that people are facing and generating nowadays is growing so rapidly that simple algorithms, such as BFS and DFS, are no longer feasible. Although Refined Online Search algorithms can scale to large graphs, they all suffer from the false positive problem. In this paper, we analyze the cause of false positive and propose an efficient High Dimensional coordinate generating method based on Graph Dominance Drawing (HD-GDD) to answer reachability queries in linear or even constant time. We conduct experiments on different graph structures and different graph sizes to fully evaluate the performance and behavior of our proposal. Empirical results demonstrate that our method outperforms state-of-the-art algorithms and can handle extensive graphs.