Provenance for aggregate queries

Abstract

We study in this paper provenance information for queries with aggregation. Provenance information was studied in the context of various query languages that do not allow for aggregation, and recent work has suggested to capture provenance by annotating the different database tuples with elements of a commutative semiring and propagating the annotations through query evaluation. We show that aggregate queries pose novel challenges rendering this approach inapplicable. Consequently, we propose a new approach, where we annotate with provenance information not just tuples but also the individual values within tuples, using provenance to describe the values computation. We realize this approach in a concrete construction, first for "simple" queries where the aggregation operator is the last one applied, and then for arbitrary (positive) relational algebra queries with aggregation; the latter queries are shown to be more challenging in this context. Finally, we use aggregation to encode queries with difference, and study the semantics obtained for such queries on provenance annotated databases.

Anytime approximation in probabilistic databases

“…The investigation of approximate probability computation for queries with aggregates via d-trees for semiring and semimodule expressions [2] is compelling since the performance of exact computation for such queries is prohibitively low. Another promising extension of this work is to consider model bounds with respect to more expressive formula languages such as decision diagrams.…”

“…Limitations (1) and (2) have been shown to be a fundamental constraint for its applicability to ranking in probabilistic databases [43]. In order to decide the relative rank of two answer tuples, it suffices to approximate their probability intervals until they are disjoint; this requires the approximation to be both deterministic and incremental.…”

“…The d-tree formalism can support sensitivity analysis and explanation for queries [32] by efficiently computing the result probability in the face of changes to the input probabilities. An extension of our framework has been recently proposed to compile expressions over semirings and semimodules such as those defining the exact probabilities of queries with aggregates in probabilistic databases [2,17].…”

A provenance framework for data-dependent process analysis

“…We then propagate them to annotations of analysis results. In other contexts (various query languages) it was shown that it suffices to compute provenance and then evaluate it (specialize it) in specific meta-domains [23,17,4].…”

“…We further analyze the complexity of computing such expressions as well as their possible sizes. Then we consider the commutation with homomorphism property, which was proven for various database query languages in [23,17,4]. The property is essential for the soundness of applying provenance to provisioning and to specialization in metadomains of interest.…”