  Detecting small sets of relevant patterns from a given dataset is a central
challenge in data mining. The relevance of a pattern is based on user-provided
criteria; typically, all patterns that satisfy certain criteria are considered
relevant. Rule-based languages like Answer Set Programming (ASP) seem
well-suited for specifying such criteria in a form of constraints. Although
progress has been made, on the one hand, on solving individual mining problems
and, on the other hand, developing generic mining systems, the existing methods
either focus on scalability or on generality. In this paper we make steps
towards combining local (frequency, size, cost) and global (various condensed
representations like maximal, closed, skyline) constraints in a generic and
efficient way. We present a hybrid approach for itemset, sequence and graph
mining which exploits dedicated highly optimized mining systems to detect
frequent patterns and then filters the results using declarative ASP. To
further demonstrate the generic nature of our hybrid framework we apply it to a
problem of approximately tiling a database. Experiments on real-world datasets
show the effectiveness of the proposed method and computational gains for
itemset, sequence and graph mining, as well as approximate tiling.
  Under consideration in Theory and Practice of Logic Programming (TPLP).
