Resource Description Framework datasets can be queried using the SPARQL language but are often irregularly structured and incomplete, which may make precise query formulation hard for users. The SPARQLAR language extends SPARQL 1.1 with two operators-APPROX and RELAX-to allow flexible querying over property paths. These operators encapsulate different dimensions of query flexibility, namely, approximation and generalisation, and they allow users to query complex, heterogeneous knowledge graphs without needing to know precisely how the data is structured. Earlier work has described the syntax, semantics, and complexity of SPARQLAR, has demonstrated its practical feasibility, but has also highlighted the need for improving the speed of query evaluation. In the present article, we focus on the design of two optimisation techniques targeted at speeding up the execution of SPARQLAR queries and on their empirical evaluation on three knowledge graphs: LUBM, DBpedia, and YAGO. We show that applying these optimisations can result in substantial improvements in the execution times of longer-running queries (sometimes by one or more orders of magnitude) without incurring significant performance penalties for fast queries.
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