TY  - JOUR
A1  - Blaesius, Thomas
A1  - Friedrich, Tobias
A1  - Schirneck, Friedrich Martin
T1  - The complexity of dependency detection and discovery in relational databases
JF  - Theoretical computer science
N2  - 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.
KW  - data profiling
KW  - enumeration complexity
KW  - functional dependency
KW  - inclusion
KW  - dependency
KW  - parameterized complexity
KW  - parsimonious reduction
KW  - transversal hypergraph
KW  - Unique column combination
KW  - W[3]-completeness
Y1  - 2021
U6  - https://doi.org/10.1016/j.tcs.2021.11.020
SN  - 0304-3975
SN  - 1879-2294
VL  - 900
SP  - 79
EP  - 96
PB  - Elsevier
CY  - Amsterdam
ER  -