3-Hop*: A Novel Hop-Based Reachability Index

A reachability query is to ask whether there exists a path between two nodes in a directed graph. To build a compact index for efficiently handling reachability queries, most existing approaches label the nodes of a small induced subgraph as the base index to cover a portion of transitive information and then either explicitly store or encode the remaining transitive information into a complementary index. Although hop-based methods have the most compact index size, they inevitably suffer from big index construction costs in terms of long indexing time and huge memory consumption. This paper proposes a new hop-based indexing scheme 3-Hop* that greatly reduces index construction costs than state-of-the-art hop-based indices. 3-Hop* first extracts a planar induces subgraph which consists of a spanning tree and the set of short non-tree edges to label graph nodes for covering more reachability information in the base index as well as providing more hop choices for building the complementary index. Then, an efficient labeling algorithm is proposed for encoding the remaining transitive information with a smaller index size based on the upper-bound density heuristic and early-stop hop selection strategy. Extensive experiments over real and synthetic datasets show that 3-Hop* is the most efficient and effective hop-based reachability indexing method scalable for large sparse graphs.