Fast reachability detection is one of the key problems in graph applications. Most of the existing works focus on creating an index and answering reachability based on that index. For these approaches, the index construction time and index size can become a concern for large graphs. More recently query-preserving graph compression has been proposed, and searching reachability over the compressed graph has been shown to be able to significantly improve query performance as well as reducing the index size. In this paper, we introduce a multilevel compression scheme for DAGs, which builds on existing compression schemes, but can further reduce the graph size for many real-world graphs. We propose an algorithm to answer reachability queries using the compressed graph. Extensive experiments with four existing state-of-the-art reachability algorithms and 12 real-world datasets demonstrate that our approach outperforms the existing methods. Experiments with synthetic datasets ensure the scalability of this approach. We also provide a discussion on possible compression for k-reachability. 194 S. Anirban et al. 1 3further reduce the size of the graph obtained by the method in [22]. Our compression utilizes a slightly modified concept of module [14], and constructs a modular decomposition tree. We show how to use the decomposition tree to answer reachability queries over the original graph efficiently. Furthermore, the decomposition tree usually takes very small space. We make the following contributions:1. We define a new concept of module, based on which we propose a multilevel graph compression scheme that compresses graphs into a smaller graph G c . 2. We organize the modules into a hierarchical structure called modular decomposition tree, and propose an efficient algorithm to utilize the tree to answer reachability queries. 3. We conduct extensive experiments with real-world graphs as well as synthetic graphs that demonstrate the advantages of our proposed approach. 4. We provide a discussion on similar compression strategies for k-reachability queries.The remainder of this paper is organized as follows. We first discuss related works in Sect. 2 and present the preliminaries in Sect. 3. Then, we give an overview of our approach and provide the theoretical foundations in Sect. 4, followed by the detailed algorithms in Sect. 5. Our experimental results are given in Sect. 6. Section 7 discusses the possibility of similar compression on k-reachability queries. We conclude our paper in Sect. 8.
Related WorkAs briefly mentioned in Sect. 1, existing approaches for answering reachability queries can be classified into indexbased and compression-based approaches.