Rapidash: Efficient Constraint Discovery via Rapid Verification (2309.12436v1)

Abstract: Denial Constraint (DC) is a well-established formalism that captures a wide range of integrity constraints commonly encountered, including candidate keys, functional dependencies, and ordering constraints, among others. Given their significance, there has been considerable research interest in achieving fast verification and discovery of exact DCs within the database community. Despite the significant advancements in the field, prior work exhibits notable limitations when confronted with large-scale datasets. The current state-of-the-art exact DC verification algorithm demonstrates a quadratic (worst-case) time complexity relative to the dataset's number of rows. In the context of DC discovery, existing methodologies rely on a two-step algorithm that commences with an expensive data structure-building phase, often requiring hours to complete even for datasets containing only a few million rows. Consequently, users are left without any insights into the DCs that hold on their dataset until this lengthy building phase concludes. In this paper, we introduce Rapidash, a comprehensive framework for DC verification and discovery. Our work makes a dual contribution. First, we establish a connection between orthogonal range search and DC verification. We introduce a novel exact DC verification algorithm that demonstrates near-linear time complexity, representing a theoretical improvement over prior work. Second, we propose an anytime DC discovery algorithm that leverages our novel verification algorithm to gradually provide DCs to users, eliminating the need for the time-intensive building phase observed in prior work. To validate the effectiveness of our algorithms, we conduct extensive evaluations on four large-scale production datasets. Our results reveal that our DC verification algorithm achieves up to 40 times faster performance compared to state-of-the-art approaches.