Containment and equivalence of well-designed SPARQL

Query containment and query equivalence constitute important computational problems in the context of static query analysis and optimization. While these problems have been intensively studied for fragments of relational calculus, almost no works exist for the semantic web query language SPARQL. In this paper, we carry out a comprehensive complexity analysis of containment and equivalence for several fragments of SPARQL: we start with the fundamental fragment of well-designed SPARQL restricted to the AND and OPTIONAL operator. We then study basic extensions in the form of the UNION operator and/or projection. The results obtained range from NP-completeness to undecidability.