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We investigate the computational complexity of minimizing the sourceside-effect in order to remove a given number of tuples from the output of aconjunctive query. In particular, given a multi-relational database $D$, aconjunctive query $Q$, and a positive integer $k$ as input, the goal is to finda 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-studieddeletion propagation problem in databases. In addition, it encapsulates thenotion of intervention for aggregate queries used in data analysis withapplications to explaining interesting observations on the output. We show adichotomy in the complexity of this problem for the class of full conjunctivequeries 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 ofthis dichotomy result already gives an exact algorithm in the easy cases; wecomplement this by giving an approximation algorithm for the hard cases of theproblem.

Generalized Deletion Propagation on Counting Conjunctive Query Answers