@article{BlaesiusFriedrichSchirneck2021,
  author    = {Blaesius, Thomas and Friedrich, Tobias and Schirneck, Friedrich Martin},
  title     = {The complexity of dependency detection and discovery in relational databases},
  series = {Theoretical computer science},
  volume    = {900},
  journal   = {Theoretical computer science},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0304-3975},
  doi       = {10.1016/j.tcs.2021.11.020},
  pages     = {79 -- 96},
  year      = {2021},
  abstract  = {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.},
  language  = {en}
}
@phdthesis{Papenbrock2017,
  author    = {Papenbrock, Thorsten},
  title     = {Data profiling - efficient discovery of dependencies},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-406705},
  school      = {Universit{\"a}t Potsdam},
  pages     = {viii, ii, 141},
  year      = {2017},
  abstract  = {Data profiling is the computer science discipline of analyzing a given dataset for its metadata. The types of metadata range from basic statistics, such as tuple counts, column aggregations, and value distributions, to much more complex structures, in particular inclusion dependencies (INDs), unique column combinations (UCCs), and functional dependencies (FDs). If present, these statistics and structures serve to efficiently store, query, change, and understand the data. Most datasets, however, do not provide their metadata explicitly so that data scientists need to profile them. While basic statistics are relatively easy to calculate, more complex structures present difficult, mostly NP-complete discovery tasks; even with good domain knowledge, it is hardly possible to detect them manually. Therefore, various profiling algorithms have been developed to automate the discovery. None of them, however, can process datasets of typical real-world size, because their resource consumptions and/or execution times exceed effective limits. In this thesis, we propose novel profiling algorithms that automatically discover the three most popular types of complex metadata, namely INDs, UCCs, and FDs, which all describe different kinds of key dependencies. The task is to extract all valid occurrences from a given relational instance. The three algorithms build upon known techniques from related work and complement them with algorithmic paradigms, such as divide \& conquer, hybrid search, progressivity, memory sensitivity, parallelization, and additional pruning to greatly improve upon current limitations. Our experiments show that the proposed algorithms are orders of magnitude faster than related work. They are, in particular, now able to process datasets of real-world, i.e., multiple gigabytes size with reasonable memory and time consumption. Due to the importance of data profiling in practice, industry has built various profiling tools to support data scientists in their quest for metadata. These tools provide good support for basic statistics and they are also able to validate individual dependencies, but they lack real discovery features even though some fundamental discovery techniques are known for more than 15 years. To close this gap, we developed Metanome, an extensible profiling platform that incorporates not only our own algorithms but also many further algorithms from other researchers. With Metanome, we make our research accessible to all data scientists and IT-professionals that are tasked with data profiling. Besides the actual metadata discovery, the platform also offers support for the ranking and visualization of metadata result sets. Being able to discover the entire set of syntactically valid metadata naturally introduces the subsequent task of extracting only the semantically meaningful parts. This is challenge, because the complete metadata results are surprisingly large (sometimes larger than the datasets itself) and judging their use case dependent semantic relevance is difficult. To show that the completeness of these metadata sets is extremely valuable for their usage, we finally exemplify the efficient processing and effective assessment of functional dependencies for the use case of schema normalization.},
  language  = {en}
}
@book{AbedjanNaumann2011,
  author    = {Abedjan, Ziawasch and Naumann, Felix},
  title     = {Advancing the discovery of unique column combinations},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  isbn      = {978-3-86956-148-6},
  issn      = {1613-5652},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-53564},
  publisher      = {Universit{\"a}t Potsdam},
  pages     = {25},
  year      = {2011},
  abstract  = {Unique column combinations of a relational database table are sets of columns that contain only unique values. Discovering such combinations is a fundamental research problem and has many different data management and knowledge discovery applications. Existing discovery algorithms are either brute force or have a high memory load and can thus be applied only to small datasets or samples. In this paper, the wellknown GORDIAN algorithm and "Apriori-based" algorithms are compared and analyzed for further optimization. We greatly improve the Apriori algorithms through efficient candidate generation and statistics-based pruning methods. A hybrid solution HCAGORDIAN combines the advantages of GORDIAN and our new algorithm HCA, and it significantly outperforms all previous work in many situations.},
  language  = {en}
}