Datasets often contain values that naturally reside in a metric space: numbers, strings, geographical locations, machine-learned embeddings in a vector space, and so on. We study the computational complexity of repairing inconsistent databases that violate integrity constraints, where the database values belong to an underlying metric space. The goal is to update the database values to retain consistency while minimizing the total distance between the original values and the repaired ones. We consider what we refer to as coincidence constraints, which include unary key constraints, inclusion constraints, foreign keys, and generally any restriction on the relationship between the numbers of cells of different labels (attributes) coinciding in a single value, for a fixed attribute set. We begin by showing that the problem is APX-hard for general metric spaces. We then present an algorithm solving the problem optimally for tree metrics, which generalize both the line metric (i.e., where repaired values are numbers) and the discrete metric (i.e., where we simply count the number of changed values). Combining our algorithm for tree metrics and a classic result on probabilistic tree embeddings, we design a (high probability) logarithmic-ratio approximation for general metrics. We also study the variant of the problem where we limit the allowed change of each individual value. In this variant, it is already NP-complete to decide the existence of any legal repair for a general metric, and we present a polynomial-time repairing algorithm for the case of a line metric.

Data regulations like GDPR require systems to support data erasure but leave the definition of "erasure" open to interpretation. This ambiguity makes compliance challenging, especially in databases where data dependencies can lead to erased data being inferred from remaining data. We formally define a precise notion of data erasure that ensures any inference about deleted data, through dependencies, remains bounded to what could have been inferred before its insertion. We design erasure mechanisms that enforce this guarantee at minimal cost. Additionally, we explore strategies to balance cost and throughput, batch multiple erasures, and proactively compute data retention times when possible. We demonstrate the practicality and scalability of our algorithms using both real and synthetic datasets.

Denial constraints (DCs) are well-known to express business rules on data. They subsume other integrity constraints (ICs), such as key constraints or functional dependencies. One can use traditional DBMS or specialized algorithms to validate such dependencies on a dataset. However, no known approach exists to detect DC violations incrementally. Data typically changes over time, and recomputing the entire violation set after every update is wasteful. Alerting data practitioners of data quality issues immediately, enables them to take measures earlier and can help prevent follow-up issues. We present Weever, the first incremental approach to detect all violations of a given set of DCs. It uses a novel index structure to process inequality predicates and a new method to plan the execution order of predicates depending on their selectivity, reducing redundant computations when handling multiple DCs. Our evaluation shows that Weever outperforms a DBMS-based baseline by up to two orders of magnitude. And in the same time that a state-of-the-art static approach takes to analyze an entire dataset, Weever processes up to 200 000 insertions.

Inclusion dependencies (INDs) are a well-known type of data dependency, specifying that the values of one column are contained in those of another column. INDs can be used for various purposes, such as foreign-key candidate selection or join partner discovery. The traditional notion of INDs is based on clean data, where the dependencies hold without exceptions. Unfortunately, data often contain errors, preventing otherwise valid INDs from being discovered. A typical response to this problem is to relax the dependency definition using a similarity measure to account for minor data errors, such as typos or different formatting. While this relaxation is known for functional dependencies, for inclusion dependencies no such relaxation has been defined. We formally introduce similarity inclusion dependencies, which relax the inclusion by demanding the existence only of sufficiently similar values. Similarity inclusion dependencies can fulfill traditional IND use cases, such as foreign-key candidate discovery, even in the presence of dirty data. We present Sawfish, the first algorithm to discover all similarity inclusion dependencies in a given dataset efficiently. Our algorithm combines approaches for the discovery of traditional INDs and string similarity joins with a novel sliding-window approach and lazy candidate validation. Our experimental evaluation shows that Sawfish can outperform a baseline by a factor of up to 6.5.