Containment of UC2RPQ: The Hard and Easy Cases

Abstract

We study the containment problem for UC2RPQ, that is, two-way Regular Path Queries, closed under conjunction, projection and union. We show a dichotomy property between PSpace-c and ExpSpace-c based on a property on the underlying graph of queries. We show that for any class C of graphs, the containment problem for queries whose underlying graph is in C is in PSpace if and only if C has bounded bridgewidth. Bridgewidth is a graph measure we introduce to this end, defined as the maximum size of a minimal edge separator of a graph. 2012 ACM Subject Classification Information systems → Graph-based database models; Information systems → Resource Description Framework (RDF); Mathematics of computing → Graph theory; Theory of computation → Formal languages and automata theory