  We investigate the computational complexity of minimizing the source
side-effect in order to remove a given number of tuples from the output of a
conjunctive query. In particular, given a multi-relational database $D$, a
conjunctive query $Q$, and a positive integer $k$ as input, the goal is to find
a minimum subset of input tuples to remove from D that would eliminate at least
$k$ output tuples from $Q(D)$. This problem generalizes the well-studied
deletion propagation problem in databases. In addition, it encapsulates the
notion of intervention for aggregate queries used in data analysis with
applications to explaining interesting observations on the output. We show a
dichotomy in the complexity of this problem for the class of full conjunctive
queries without self-joins by giving a characterization on the structure of $Q$
that makes the problem either polynomial-time solvable or NP-hard. Our proof of
this dichotomy result already gives an exact algorithm in the easy cases; we
complement this by giving an approximation algorithm for the hard cases of the
problem.
