3-HOP: A High-compression Indexing Scheme For Reachability Query

Abstract

Reachability queries on large directed graphs have attracted much attention recently. The existing work either uses spanning structures, such as chains or trees, to compress the complete transitive closure, or utilizes the 2-hop strategy to describe the reachability. Almost all of these approaches work well for very sparse graphs. However, the challenging problem is that as the ratio of the number of edges to the number of vertices increases, the size of the compressed transitive closure grows very large. In this paper, we propose a new 3-hop indexing scheme for directed graphs with higher density. The basic idea of 3-hop indexing is to use chain structures in combination with hops to minimize the number of structures that must be indexed. Technically, our goal is to find a 3-hop scheme over dense DAGs (directed acyclic graphs) with minimum index size. We develop an efficient algorithm to discover a <i>transitive closure contour</i>, which yields near optimal index size. Empirical studies show that our 3-hop scheme has much smaller index size than state-of-the-art reachability query schemes such as 2-hop and path-tree when DAGs are not very sparse, while our query time is close to path-tree, which is considered to be one of the best reachability query schemes.