@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}
}
@article{BlaesiusFriedrichLischeidetal.2022,
  author    = {Bl{\"a}sius, Thomas and Friedrich, Tobias and Lischeid, Julius and Meeks, Kitty and Schirneck, Friedrich Martin},
  title     = {Efficiently enumerating hitting sets of hypergraphs arising in data profiling},
  series = {Journal of computer and system sciences : JCSS},
  volume    = {124},
  journal   = {Journal of computer and system sciences : JCSS},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0022-0000},
  doi       = {10.1016/j.jcss.2021.10.002},
  pages     = {192 -- 213},
  year      = {2022},
  abstract  = {The transversal hypergraph problem asks to enumerate the minimal hitting sets of a hypergraph. If the solutions have bounded size, Eiter and Gottlob [SICOMP'95] gave an algorithm running in output-polynomial time, but whose space requirement also scales with the output. We improve this to polynomial delay and space. Central to our approach is the extension problem, deciding for a set X of vertices whether it is contained in any minimal hitting set. We show that this is one of the first natural problems to be W[3]-complete. We give an algorithm for the extension problem running in time O(m(vertical bar X vertical bar+1) n) and prove a SETH-lower bound showing that this is close to optimal. We apply our enumeration method to the discovery problem of minimal unique column combinations from data profiling. Our empirical evaluation suggests that the algorithm outperforms its worst-case guarantees on hypergraphs stemming from real-world databases.},
  language  = {en}
}