Efficient Enumeration of Recursive Plans in Transformation-based Query Optimizers

Query optimizers built on the transformation-based Volcano/Cascades framework are used in many database systems. Transformations proposed earlier on the logical query dag (LQDAG) data structure, which is key in such a framework, are restricted to recursion-free queries. We propose the recursive logical query dag (RLQDAG) which extends the LQDAG with the ability to capture and transform recursive queries, leveraging recent developments in recursive relational algebra. Specifically, this extension includes: (i) the ability of capturing and transforming sets of recursive relational terms thanks to (ii) annotated equivalence nodes used for guiding transformations that are more complex in the presence of recursion; and (iii) RLQDAG rewrite rules that transform sets of subterms in a grouped manner, instead of transforming individual terms in a sequential manner; and that (iv) incrementally update the necessary annotations. Core concepts of the RLQDAG are formalized using a syntax and formal semantics with a particular focus on subterm sharing and recursion. The result is a clean generalization of the LQDAG, enabling efficient explorations of plan spaces for recursive queries. An implementation of the proposed approach shows significant performance gains compared to the state-of-the-art.