The tractability frontier of well-designed SPARQL queries

We study the complexity of query evaluation of SPARQL queries. We focus on the fundamental fragment of welldesigned SPARQL restricted to the AND, OPTIONAL and UNION operators. Our main result is a structural characterisation of the classes of well-designed queries that can be evaluated in polynomial time. In particular, we introduce a new notion of width called domination width, which relies on the well-known notion of treewidth. We show that, under some complexity theoretic assumptions, the classes of welldesigned queries that can be evaluated in polynomial time are precisely those of bounded domination width.