The tractability frontier of well-designed SPARQL queries
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We study the complexity of query evaluation of SPARQL queries. We focus on the fundamental fragment of well-designed 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 well-designed queries that can be evaluated in polynomial time are precisely those of bounded domination width.
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