On the Complexity of Insertion Propagation with Functional Dependency Constraints

Abstract

Insertion propagation problem is a class of view update problem in relational databases [1]. Given a source database D, a monotone relational algebraic query Q, and the view V generated by the query Q(D), insertion propagation problem is to find a set $\varDelta D$ of tuples whose insertion into D will add the given tuples $\varDelta V$ into the view V via Q without producing side-effect on view. In this paper, we consider the fd-restricted version insertion propagation problem ‘${\textit{fd}}{\text {-}}\textsf {vsef}{\text {-}}{\textsf {ip}}$’, in which we aim to find the $\varDelta D$ not only view side-effect free but also without introducing inconsistency with respect to the predefined functional dependencies. We study both data and combined complexity of ${\textit{fd}}{\text {-}}\textsf {vsef}{\text {-}}{\textsf {ip}}$ under both single and group insertion. Interestingly, the problem ranges from $\mathsf {PTime}$ to $\mathsf {\Sigma }_{2}^{\mathrm {P}}$-$\mathsf {complete}$, for queries in different classes in either complexity aspect.We show that the fd-restricted version will be harder to get the optimal solution, contrary to its counterpart under deletion. Our study of this fd-restricted version insertion propagation problem generalize the computational issues involved in data lineage – the process by which databases updated through view insertion under fd.