GRAIL

Abstract

Given a large directed graph, rapidly answering reachability queries between source and target nodes is an important problem. Existing methods for reachability trade-off indexing time and space versus query time performance. However, the biggest limitation of existing methods is that they simply do not scale to very large real-world graphs. We present a very simple, but scalable reachability index, called GRAIL, that is based on the idea of randomized interval labeling, and that can effectively handle very large graphs. Based on an extensive set of experiments, we show that while more sophisticated methods work better on small graphs, GRAIL is the only index that can scale to millions of nodes and edges. GRAIL has linear indexing time and space, and the query time ranges from constant time to being linear in the graph order and size.