Extended high dimensional indexing approach for reachability queries on very large graphs

Abstract

Given a directed acyclic graph G = (V,A) and two vertices u, v ∈ V , the reachability problem is to answer if there is a path from u to v in the graph. In the context of very large graphs, with millions of vertices and a series of queries to be answered, it is not practical to search the graph for each query. On the other hand, the storage of the full transitive closure of the graph is also impractical due to its O(|V |2) size. Scalable approaches aim to create indices used to prune the search during its execution. Negative indices may be able to determine (in constant time) that a query has a negative answer while positive indices may determine (again in constant time) that a query has a positive answer. In this paper we propose novel scalable approach called LYNX that uses a large number of topological sorts of G as a negative cut index without degrading the query time. A similar strategy is applied regarding a positive cut index. In addition, LYNX proposes a user-defined index size that enables the user to control the ratio between negative and positive cuts depending on the expected query pattern. We show by computational experiments that LYNX consistently outperforms the state-of-the-art approach in terms of query-time using the same index-size for graphs with high reachability ratio. In intelligent computer systems that rely on frequent tests of connectivity in graphs, LYNX can reduce the time delay experience by end users through a reduced query time. This comes at the expense of an increased setup time whenever the underlying graph is updated. Keywords: directed acyclic graphs, topological sorts, reachability queries, graph indexing