@phdthesis{Schirneck2022,
  author    = {Schirneck, Friedrich Martin},
  title     = {Enumeration algorithms in data profiling},
  doi       = {10.25932/publishup-55672},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-556726},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xiv, 192},
  year      = {2022},
  abstract  = {Data profiling is the extraction of metadata from relational databases. An important class of metadata are multi-column dependencies. They come associated with two computational tasks. The detection problem is to decide whether a dependency of a given type and size holds in a database. The discovery problem instead asks to enumerate all valid dependencies of that type. We investigate the two problems for three types of dependencies: unique column combinations (UCCs), functional dependencies (FDs), and inclusion dependencies (INDs). We first treat the parameterized complexity of the detection variants. We prove that the detection of UCCs and FDs, respectively, is W[2]-complete when parameterized by the size of the dependency. The detection of INDs is shown to be one of the first natural W[3]-complete problems. We further settle the enumeration complexity of the three discovery problems by presenting parsimonious equivalences with well-known enumeration problems. Namely, the discovery of UCCs is equivalent to the famous transversal hypergraph problem of enumerating the hitting sets of a hypergraph. The discovery of FDs is equivalent to the simultaneous enumeration of the hitting sets of multiple input hypergraphs. Finally, the discovery of INDs is shown to be equivalent to enumerating the satisfying assignments of antimonotone, 3-normalized Boolean formulas. In the remainder of the thesis, we design and analyze discovery algorithms for unique column combinations. Since this is as hard as the general transversal hypergraph problem, it is an open question whether the UCCs of a database can be computed in output-polynomial time in the worst case. For the analysis, we therefore focus on instances that are structurally close to databases in practice, most notably, inputs that have small solutions. The equivalence between UCCs and hitting sets transfers the computational hardness, but also allows us to apply ideas from hypergraph theory to data profiling. We devise an discovery algorithm that runs in polynomial space on arbitrary inputs and achieves polynomial delay whenever the maximum size of any minimal UCC is bounded. Central to our approach is the extension problem for minimal hitting sets, that is, to decide for a set of vertices whether they are contained in any minimal solution. We prove that this is yet another problem that is complete for the complexity class W[3], when parameterized by the size of the set that is to be extended. We also give several conditional lower bounds under popular hardness conjectures such as the Strong Exponential Time Hypothesis (SETH). The lower bounds suggest that the running time of our algorithm for the extension problem is close to optimal. We further conduct an empirical analysis of our discovery algorithm on real-world databases to confirm that the hitting set perspective on data profiling has merits also in practice. We show that the resulting enumeration times undercut their theoretical worst-case bounds on practical data, and that the memory consumption of our method is much smaller than that of previous solutions. During the analysis we make two observations about the connection between databases and their corresponding hypergraphs. On the one hand, the hypergraph representations containing all relevant information are usually significantly smaller than the original inputs. On the other hand, obtaining those hypergraphs is the actual bottleneck of any practical application. The latter often takes much longer than enumerating the solutions, which is in stark contrast to the fact that the preprocessing is guaranteed to be polynomial while the enumeration may take exponential time. To make the first observation rigorous, we introduce a maximum-entropy model for non-uniform random hypergraphs and prove that their expected number of minimal hyperedges undergoes a phase transition with respect to the total number of edges. The result also explains why larger databases may have smaller hypergraphs. Motivated by the second observation, we present a new kind of UCC discovery algorithm called Hitting Set Enumeration with Partial Information and Validation (HPIValid). It utilizes the fast enumeration times in practice in order to speed up the computation of the corresponding hypergraph. This way, we sidestep the bottleneck while maintaining the advantages of the hitting set perspective. An exhaustive empirical evaluation shows that HPIValid outperforms the current state of the art in UCC discovery. It is capable of processing databases that were previously out of reach for data profiling.},
  language  = {en}
}
@phdthesis{Shaabani2020,
  author    = {Shaabani, Nuhad},
  title     = {On discovering and incrementally updating inclusion dependencies},
  doi       = {10.25932/publishup-47186},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-471862},
  school      = {Universit{\"a}t Potsdam},
  pages     = {119},
  year      = {2020},
  abstract  = {In today's world, many applications produce large amounts of data at an enormous rate. Analyzing such datasets for metadata is indispensable for effectively understanding, storing, querying, manipulating, and mining them. Metadata summarizes technical properties of a dataset which rang from basic statistics to complex structures describing data dependencies. One type of dependencies is inclusion dependency (IND), which expresses subset-relationships between attributes of datasets. Therefore, inclusion dependencies are important for many data management applications in terms of data integration, query optimization, schema redesign, or integrity checking. So, the discovery of inclusion dependencies in unknown or legacy datasets is at the core of any data profiling effort. For exhaustively detecting all INDs in large datasets, we developed S-indd++, a new algorithm that eliminates the shortcomings of existing IND-detection algorithms and significantly outperforms them. S-indd++ is based on a novel concept for the attribute clustering for efficiently deriving INDs. Inferring INDs from our attribute clustering eliminates all redundant operations caused by other algorithms. S-indd++ is also based on a novel partitioning strategy that enables discording a large number of candidates in early phases of the discovering process. Moreover, S-indd++ does not require to fit a partition into the main memory--this is a highly appreciable property in the face of ever-growing datasets. S-indd++ reduces up to 50\% of the runtime of the state-of-the-art approach. None of the approach for discovering INDs is appropriate for the application on dynamic datasets; they can not update the INDs after an update of the dataset without reprocessing it entirely. To this end, we developed the first approach for incrementally updating INDs in frequently changing datasets. We achieved that by reducing the problem of incrementally updating INDs to the incrementally updating the attribute clustering from which all INDs are efficiently derivable. We realized the update of the clusters by designing new operations to be applied to the clusters after every data update. The incremental update of INDs reduces the time of the complete rediscovery by up to 99.999\%. All existing algorithms for discovering n-ary INDs are based on the principle of candidate generation--they generate candidates and test their validity in the given data instance. The major disadvantage of this technique is the exponentially growing number of database accesses in terms of SQL queries required for validation. We devised Mind2, the first approach for discovering n-ary INDs without candidate generation. Mind2 is based on a new mathematical framework developed in this thesis for computing the maximum INDs from which all other n-ary INDs are derivable. The experiments showed that Mind2 is significantly more scalable and effective than hypergraph-based algorithms.},
  language  = {en}
}
@phdthesis{Kruse2018,
  author    = {Kruse, Sebastian},
  title     = {Scalable data profiling},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-412521},
  school      = {Universit{\"a}t Potsdam},
  pages     = {ii, 156},
  year      = {2018},
  abstract  = {Data profiling is the act of extracting structural metadata from datasets. Structural metadata, such as data dependencies and statistics, can support data management operations, such as data integration and data cleaning. Data management often is the most time-consuming activity in any data-related project. Its support is extremely valuable in our data-driven world, so that more time can be spent on the actual utilization of the data, e. g., building analytical models. In most scenarios, however, structural metadata is not given and must be extracted first. Therefore, efficient data profiling methods are highly desirable. Data profiling is a computationally expensive problem; in fact, most dependency discovery problems entail search spaces that grow exponentially in the number of attributes. To this end, this thesis introduces novel discovery algorithms for various types of data dependencies - namely inclusion dependencies, conditional inclusion dependencies, partial functional dependencies, and partial unique column combinations - that considerably improve over state-of-the-art algorithms in terms of efficiency and that scale to datasets that cannot be processed by existing algorithms. The key to those improvements are not only algorithmic innovations, such as novel pruning rules or traversal strategies, but also algorithm designs tailored for distributed execution. While distributed data profiling has been mostly neglected by previous works, it is a logical consequence on the face of recent hardware trends and the computational hardness of dependency discovery. To demonstrate the utility of data profiling for data management, this thesis furthermore presents Metacrate, a database for structural metadata. Its salient features are its flexible data model, the capability to integrate various kinds of structural metadata, and its rich metadata analytics library. We show how to perform a data anamnesis of unknown, complex datasets based on this technology. In particular, we describe in detail how to reconstruct the schemata and assess their quality as part of the data anamnesis. The data profiling algorithms and Metacrate have been carefully implemented, integrated with the Metanome data profiling tool, and are available as free software. In that way, we intend to allow for easy repeatability of our research results and also provide them for actual usage in real-world data-related projects.},
  language  = {en}
}