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## Section: New Results

### Extending the SPARQL Algebra for the optimization of Property Paths

In this work [22], [21], we propose a new algebra, $\mu$-algebra, inspired by works on the relational algebra, SQL and NoSQL languages (especially SPARQL) along with a prototype implementation of a SPARQL optimizer based on this algebra1. Our algebra has the following properties: (1) It subsumes the SPARQL Algebra (under the set semantics) with a more general recursion. (2) SPARQL with Property Paths can be e ciently translated to this algebra. (3) We have a type system and rewriting rules for terms of this algebra that allow optimization, notably of terms involving recursion. We illustrate the differences and the benefits of our approach on recursive query optimization. While a generic approach often comes at the cost of performance, we experimentally show that this approach actually leads to more efficient evaluation of queries with Property Paths. We also show that our approach produces Query Execution Plans (QEP) that are not considered by other existing approaches.