@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} } @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} } @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} } @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{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} }