A dichotomy in the complexity of deletion propagation with functional dependencies

A classical variant of the view-update problem is deletion propagation, where tuples from the database are deleted in order to realize a desired deletion of a tuple from the view. This operation may cause a (sometimes necessary) side effect---deletion of additional tuples from the view, besides the intentionally deleted one. The goal is to propagate deletion so as to maximize the number of tuples that remain in the view. In this paper, a view is defined by a self-join-free conjunctive query (sjf-CQ) over a schema with functional dependencies. A condition is formulated on the schema and view definition at hand, and the following dichotomy in complexity is established. If the condition is met, then deletion propagation is solvable in polynomial time by an extremely simple algorithm (very similar to the one observed by Buneman et al.). If the condition is violated, then the problem is NP-hard, and it is even hard to realize an approximation ratio that is better than some constant; moreover, deciding whether there is a side-effect-free solution is NP-complete. This result generalizes a recent result by Kimelfeld et al., who ignore functional dependencies. For the class of sjf-CQs, it also generalizes a result by Cong et al., stating that deletion propagation is in polynomial time if keys are preserved by the view.