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This paper addresses the problem of failing $$\\mathtt {RDF}$$ queries. Query relaxation is one of the cooperative techniques that allows providing users with alternative answers instead of an empty result. While previous works on query relaxation over $$\\mathtt {RDF}$$ data have focused on defining new relaxation operators, we investigate in this paper techniques to find the parts of an $$\\mathtt {RDF}$$ query that are responsible of its failure. Finding such subqueries, named Minimal Failing Subqueries$$\\mathtt {MFSs}$$, is of great interest to efficiently perform the relaxation process. We propose two algorithmic approaches for computing $$\\mathtt {MFSs}$$. The first approach $$\\mathtt {LBA}$$ intelligently leverages the subquery lattice of the initial $$\\mathtt {RDF}$$ query while the second approach $$\\mathtt {MBA}$$ is based on a particular matrix that improves the performance of $$\\mathtt {LBA}$$. Our approaches also compute a particular kind of relaxed RDF queries, called Maximal Succeeding Subqueries$$\\mathtt {XSSs}$$. $$\\mathtt {XSSs}$$ are subqueries with a maximal number of triple patterns of the initial query. To validate our approaches, a set of thorough experiments is conducted on the $$\\mathtt {LUBM}$$ benchmark and a comparative study with other approaches is done.

Cooperative Techniques for SPARQL Query Relaxation in RDF Databases