DAG Reduction

Abstract

Answering reachability queries is one of the fundamental graph operations. The existing approaches build indexes and answer reachability queries on a directed acyclic graph (DAG) G, which is constructed by coalescing each strongly connected component of the given directed graph G into a node of G. Considering that G can still be large to be processed efficiently, there are studies to further reduce G to a smaller graph. However, these approaches suffer from either inefficiency in answering reachability queries, or cannot scale to large graphs. In this paper, we study DAG reduction to accelerate reachability query processing, which reduces the size of G by computing transitive reduction (TR) followed by computing equivalence reduction (ER). For ER, we propose a divide-and-conquer algorithm, namely linear-ER. Given the result Gt of TR, linear-ER gets a smaller DAG Ge in linear time based on equivalence relationship between nodes in G. Our DAG reduction approaches (TR and ER) significantly improve the cost of time and space, and can be scaled to large graphs. We confirm the efficiency of our approaches by extensive experimental studies for TR, ER, and reachability query processing using 20 real datasets.