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Multi-column dependencies in relational databases come associated with two different computational tasks. The detection problem is to decide whether a dependency of a certain type and size holds in a given database, the discovery problem asks to enumerate all valid dependencies of that type. We settle the complexity of both of these problems for unique column combinations (UCCs), functional dependencies (FDs), and inclusion dependencies (INDs). We show that the detection of UCCs and FDs is W[2]-complete when parameterized by the solution size. The discovery of inclusion-wise minimal UCCs is proven to be equivalent under parsimonious reductions to the transversal hypergraph problem of enumerating the minimal hitting sets of a hypergraph. The discovery of FDs is equivalent to the simultaneous enumeration of the hitting sets of multiple input hypergraphs. We further identify the detection of INDs as one of the first natural W[3]-complete problems. The discovery of maximal INDs is shown to be equivalent to enumerating the maximal satisfying assignments of antimonotone, 3-normalized Boolean formulas.
With the advent of big data and data lakes, data are often integrated from multiple sources. Such integrated data are often of poor quality, due to inconsistencies, errors, and so forth. One way to check the quality of data is to infer functional dependencies (fds). However, in many modern applications it might be necessary to extract properties and relationships that are not captured through fds, due to the necessity to admit exceptions, or to consider similarity rather than equality of data values. Relaxed fds (rfds) have been introduced to meet these needs, but their discovery from data adds further complexity to an already complex problem, also due to the necessity of specifying similarity and validity thresholds. We propose Domino, a new discovery algorithm for rfds that exploits the concept of dominance in order to derive similarity thresholds of attribute values while inferring rfds. An experimental evaluation on real datasets demonstrates the discovery performance and the effectiveness of the proposed algorithm.