  Studying the computational complexity of problems is one of the - if not the
- fundamental questions in computer science. Yet, surprisingly little is known
about the computational complexity of many central problems in data mining. In
this paper we study frequency-based problems and propose a new type of
reduction that allows us to compare the complexities of the maximal frequent
pattern mining problems in different domains (e.g. graphs or sequences). Our
results extend those of Kimelfeld and Kolaitis [ACM TODS, 2014] to a broader
range of data mining problems. Our results show that, by allowing constraints
in the pattern space, the complexities of many maximal frequent pattern mining
problems collapse. These problems include maximal frequent subgraphs in
labelled graphs, maximal frequent itemsets, and maximal frequent subsequences
with no repetitions. In addition to theoretical interest, our results might
yield more efficient algorithms for the studied problems.
