Efficiently Approximating Query Optimizer Plan Diagrams

Given a parametrized n-dimensional SQL query template and a choice of query optimizer, a plan diagram is a color-coded pictorial enumeration of the execution plan choices of the optimizer over the query parameter space. These diagrams have proved to be a powerful metaphor for the analysis and redesign of modern optimizers, and are gaining currency in diverse industrial and academic institutions. However, their utility is adversely impacted by the impractically large computational overheads incurred when standard brute-force exhaustive approaches are used for producing fine-grained diagrams on high-dimensional query templates. In this paper, we investigate strategies for efficiently producing close approximations to complex plan diagrams. Our techniques are customized to the features available in the optimizer's API, ranging from the generic optimizers that provide only the optimal plan for a query, to those that also support costing of sub-optimal plans and enumerating rank-ordered lists of plans. The techniques collectively feature both random and grid sampling, as well as inference techniques based on nearest-neighbor classifiers, parametric query optimization and plan cost monotonicity. Extensive experimentation with a representative set of TPC-H and TPC-DS-based query templates on industrial-strength optimizers indicates that our techniques are capable of delivering 90% accurate diagrams while incurring less than 15% of the computational overheads of the exhaustive approach. In fact, for full-featured optimizers, we can guarantee zero error with less than 10% overheads. These approximation techniques have been implemented in the publicly available Picasso optimizer visualization tool.