Reachability queries ask whether a vertex can reach another vertex on large directed graphs. It is one of the most fundamental graph operators and has attracted researchers in both academics and industry to study it. The main technical challenge is to support fast reachability queries by efficient managing the three main costs: the index construction time, the index size and the query processing time on large/small and sparse/dense graphs. As real world graphs grow bigger in size, these problems remain open challenges that demand high performance solutions. In this article, we propose aMulti-Dimensional Graph Labelingapproach (calledMGTag) to supporting fast reachability queries.MGTagis novel in three aspects. First, it recursively partitions a graph into multiple subgraphs with disjoint vertex sets, called non-shared graphs, and several inter-partition edges, called cross-edges. Second, we build a four-dimensional label – one dimension of layer, one dimension of non-shared graph and two dimensions of interval for each vertex in non-shared graphs. Finally, with the four-dimensional labeling scheme, we design algorithms to answer reachability queries efficiently. The extensive experiments on 28 large/small and dense/sparse graphs show that building the high dimensional index is quickly and the index size is also competitive compared with most of the state-of-the-art approaches. The results also show that our approach is more scalable and efficient than the state-of-the-art approaches in answering reachability queries on large/small and sparse/dense graphs.

Reachability query asks whether a vertex can reach another vertex on large directed graphs. It is one of the most fundamental graph operators and has attracted many researchers to study it. Although there are many approaches solving this problem, it still remains a challenging problem when it comes to leverage the three main costs: the index construction time, the index size, and the query time on large and dense graphs. In this paper, we propose a High Dimension Graph Labeling approach to answer reachability queries. First, we recursively partition a graph into disjoint non-shared graphs, among which there are no common vertices, and cross edges. Second, we build a four dimensional label - one dimension of layer, one dimension of sub-graph and two dimensions of interval for each vertex. With the layer label and the sub-graph label, we can determine the positions (non-shared graphs) of any two vertices. Two dimensional interval label is used to assist to answer the reachability queries for vertex pair in those non-shared graphs. Finally, we design algorithms to answer researchability queries efficiently. In order to speed up query answering, we also build two directional labels: up and down labels to filter vertices quickly. The extensive experiments on 28 large/small and dense/sparse graphs show that building the high dimensional index is quickly and the index size is also competitive compared with most of the state of the art approaches. The results also show that our approach is more scalable and efficient than the state-of-the-art approaches in answering reachability queries.