@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{ShiSchirneckFriedrichetal.2018, author = {Shi, Feng and Schirneck, Friedrich Martin and Friedrich, Tobias and K{\"o}tzing, Timo and Neumann, Frank}, title = {Reoptimization time analysis of evolutionary algorithms on linear functions under dynamic uniform constraints}, series = {Algorithmica : an international journal in computer science}, volume = {82}, journal = {Algorithmica : an international journal in computer science}, number = {10}, publisher = {Springer}, address = {New York}, issn = {0178-4617}, doi = {10.1007/s00453-020-00739-x}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-605295}, pages = {3117 -- 3123}, year = {2018}, abstract = {Rigorous runtime analysis is a major approach towards understanding evolutionary computing techniques, and in this area linear pseudo-Boolean objective functions play a central role. Having an additional linear constraint is then equivalent to the NP-hard Knapsack problem, certain classes thereof have been studied in recent works. In this article, we present a dynamic model of optimizing linear functions under uniform constraints. Starting from an optimal solution with respect to a given constraint bound, we investigate the runtimes that different evolutionary algorithms need to recompute an optimal solution when the constraint bound changes by a certain amount. The classical (1+1) EA and several population-based algorithms are designed for that purpose, and are shown to recompute efficiently. Furthermore, a variant of the (1+(λ,λ))GA for the dynamic optimization problem is studied, whose performance is better when the change of the constraint bound is small.}, language = {en} } @article{BirnickBlaesiusFriedrichetal.2020, author = {Birnick, Johann and Bl{\"a}sius, Thomas and Friedrich, Tobias and Naumann, Felix and Papenbrock, Thorsten and Schirneck, Friedrich Martin}, title = {Hitting set enumeration with partial information for unique column combination discovery}, series = {Proceedings of the VLDB Endowment}, volume = {13}, journal = {Proceedings of the VLDB Endowment}, number = {11}, publisher = {Association for Computing Machinery}, address = {[New York, NY]}, issn = {2150-8097}, doi = {10.14778/3407790.3407824}, pages = {2270 -- 2283}, year = {2020}, abstract = {Unique column combinations (UCCs) are a fundamental concept in relational databases. They identify entities in the data and support various data management activities. Still, UCCs are usually not explicitly defined and need to be discovered. State-of-the-art data profiling algorithms are able to efficiently discover UCCs in moderately sized datasets, but they tend to fail on large and, in particular, on wide datasets due to run time and memory limitations.
In this paper, we introduce HPIValid, a novel UCC discovery algorithm that implements a faster and more resource-saving search strategy. HPIValid models the metadata discovery as a hitting set enumeration problem in hypergraphs. In this way, it combines efficient discovery techniques from data profiling research with the most recent theoretical insights into enumeration algorithms. Our evaluation shows that HPIValid is not only orders of magnitude faster than related work, it also has a much smaller memory footprint.}, 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} }