Providing Fast Reachability Query Services With MGTag: A Multi-Dimensional Graph Labeling Method

Abstract

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 paper, we propose a Multi-Dimensional Graph Labeling approach (called MGTag) to supporting fast reachability queries. MGTag is 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.