On tractable query evaluation for SPARQL

Despite much work within the last decade on foundational properties of SPARQL – the standard query language for RDF data – rather little is known about the exact limits of tractability for this language. In particular, this is the case for SPARQL queries that contain the OPTIONALoperator, even though it is one of the most intensively studied features of SPARQL. The aim of our work is to provide a more thorough picture of tractable classes of SPARQL queries. In general, SPARQL query evaluation is PSPACE-complete in combined complexity, and it remains PSPACE-hard already for queries containing only the OPTIONAL-operator. To amend this situation, research has focused on “well-designed SPARQL queries” and their recent generalization “weakly well-designed SPARQL queries”. For these two fragments the evaluation problem is coNP-complete in the absence of projection and Σ2P-complete otherwise. Moreover, they have been shown to contain most SPARQL queries asked in practical settings. In this paper, we study tractable classes of weakly well-designed queries in parameterized complexity considering the equivalent formulation as pattern trees. We give a complete characterization of the tractable classes in the case without projection. Moreover, we show a characterization of all tractable classes of simple well-designed pattern trees in the presence of projection.