On the Evaluation of Large and Sparse Graph Reachability Queries

Abstract

Given a directed graph G with n nodes and e edges, to check whether a node v is reachable from another node u through a path is often required. Such a problem is fundamental to numerous applications, including geographic navigation, Internet routing, ontology queries based on RDF/OWL, and metabolic network, as well as XML indexing. Among them, some involve huge but sparse graphs and require fast answering of reachability queries. In this paper, we propose a novel method called core labeling to handle reachability queries for massive, sparse graphs. The goal is to optimize both query time and labeling time. Our method consists of two schemes: Core-I and Core-II. For the Core-I labeling scheme, both the time and space requirements are bounded by O(n + e + s·b), where s is the number of the start nodes of all non-tree edges (edges that do not appear in the spanning tree of G); andb is the width of a subgraph of G. The size of that subgraph is bounded by O(t), where t is the number of all the non-tree edges. The query time of Core-I is bounded by O(logb). The Core-II labeling scheme has constant query time, but the labeling time is increased to O(n + e + s·b·logb).