New Results on the Complexity of Deletion Propagation

Abstract

The problem of deletion propagation in relational database has been studied in database community for decades, where tuples are deleted from the source database in order to realize a desired removal of tuples from the result of a certain query. The deletion may result in unexpected view and source side effects. To minimize the side effects, we study two problems: MaxDP which is to seek a deletion of source tuples that maximizes query result remaining after deleting some view tuples, and MinSD which is to seek a minimum set of source tuples that should be deleted. Two problems have been proved that they are polynomially tractable for conjunctive queries without existential variables ($\forall$-CQs). However, for $\forall$-CQs, the complexity of MaxDP is still unknown for deletion forbidden restriction, and so does MinSD in the presence of inclusion dependencies. In this paper, new complexity results are obtained on both problems for $\forall$-CQs. MaxDP is turned out to be not only NP-complete, but also NP-hard to approximate within $O(n^{1/5-\epsilon })$ for any constant $\epsilon >0$ when the deletion of some tuples is forbidden. We then show that even for linear queries, MinSD is no longer polynomially tractable in the presence of inclusion dependencies. The results shows that the complexity of deletion propagation is very sensitive to the presence of some simple constraints.