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Counting queries are ubiquitous in database systems, particularly for driving internal system optimization. Learned models for cardinality estimation rely heavily on large-scale training data, yet generating such data by executing massive batches of counting queries is expensive. We propose BaCon, an efficient algorithm for batch evaluation of counting queries on top of a database system, without modifying its internals. BaCon integrates the idea of factorized databases with a workload-aware domain quantization strategy, allowing it to evaluate batches of counting queries using compact data structures rather than materializing massive join results. BaCon’s design is compatible with most database management system, and we have implemented it as a client-side application on PostgreSQL with a lightweight C-language UDF (user-defined function). This implementation delivers speedups between 2× and 178× over baselines and good performance across various workloads, making training and maintenance of learned cardinality estimation models significantly more practical. 

Query optimizers must efficiently choose a query plan using noisy estimates of cardinalities. We study robust query optimization, where the optimizer is made aware of the uncertainty in cardinality estimates and needs to select the most ''robust'' plan. A key empirical observation is that a small set of plans often suffices as robust plan candidates for all queries following a given template. We formalize this phenomenon by introducing coresets of plans and extend this notion to robust coresets, which incorporate uncertainty. We prove positive and negative results on the sizes of such coresets for common cost-function classes. Because our lower bounds suggest that the size of a coreset can be large in the worst case, we exploit the fact that in practice queries arise from workload distributions, rather than being arbitrary. We present algorithms that construct workload-aware coresets whose size and performance closely match those of the optimal workload-specific coresets. 

Abstract: Let K be a compact, centrally-symmetric, strictly-convex region in ℝ³, which is a semi-algebraic set of constant complexity, i.e. the unit ball of a corresponding metric, denoted as ‖⋅‖_K. Let 𝒦 be a set of n homothetic copies of K. This paper contains two main sets of results: (i) For a storage parameter s ∈ [n,n³], 𝒦 can be preprocessed in O^*(s) expected time into a data structure of size O^*(s), so that for a query homothet K₀ of K, an intersection-detection query (determine whether K₀ intersects any member of 𝒦, and if so, report such a member) or a nearest-neighbor query (return the member of 𝒦 whose ‖⋅‖_K-distance from K₀ is smallest) can be answered in O^*(n/s^{1/3}) time; all k homothets of 𝒦 intersecting K₀ can be reported in additional O(k) time. In addition, the data structure supports insertions/deletions in O^*(s/n) amortized expected time per operation. Here the O^*(⋅) notation hides factors of the form n^ε, where ε > 0 is an arbitrarily small constant, and the constant of proportionality depends on ε. (ii) Let 𝒢(𝒦) denote the intersection graph of 𝒦. Using the above data structure, breadth-first or depth-first search on 𝒢(𝒦) can be performed in O^*(n^{3/2}) expected time. Combining this result with the so-called shrink-and-bifurcate technique, the reverse-shortest-path problem in a suitably defined proximity graph of 𝒦 can be solved in O^*(n^{62/39}) expected time. Dijkstra’s shortest-path algorithm, as well as Prim’s MST algorithm, on a ‖⋅‖_K-proximity graph on n points in ℝ³, with edges weighted by ‖⋅‖_K, can also be performed in O^*(n^{3/2}) time. 

Parametric Query Optimization (PQO) is an important problem in database systems, yet existing approaches suffer from high training costs, sensitivity to estimation errors, and vulnerability to severe performance regressions. This paper introduces PAR²QO (PARametric Penalty-Aware Robust Query Optimization), a system that integrates robust query optimization into PQO. PAR²QO strategically obtains plans from a well-balanced set of probe locations informed by the workload, and caches them as plan-penalty profiles. At runtime, PAR²QO selects the plan with the lowest expected penalty, explicitly accounting for selectivity uncertainties. Extensive experiments show that PAR²QO delivers significant speedups over existing methods while ensuring robustness against performance degradation. Additionally, we introduceCARVER, a workload generator aimed at covering possible cardinalities of subqueries. Not only does CARVER provide a more comprehensive way to evaluate PQO methods, but when used for training learned methods, it can also enhance their generalizability and stability.