The resilience of a Boolean query on a database is the minimum number of tuples that need to be deleted from the input tables in order to make the query false. A solution to this problem immediately translates into a solution for the more widely known problem of deletion propagation with source-side effects. In this paper, we give several novel results on the hardness of the resilience problem for conjunctive queries with self-joins, and, more specifically, we present a dichotomy result for the class of single-self-join binary queries with exactly two repeated relations occurring in the query. Unlike in the self-join free case, the concept of triad is not enough to fully characterize the complexity of resilience. We identify new structural properties, namely chains, confluences and permutations, which lead to various NP-hardness results. We also give novel involved reductions to network flow to show certain cases are in P. Although restricted, our results provide important insights into the problem of self-joins that we hope can help solve the general case of all conjunctive queries with self-joins in the future.

Several research thrusts in the area of data management have focused on understanding how changes in the data affect the output of a view or standing query. Example applications are explaining query results, propagating updates through views, and anonymizing datasets. An important aspect of this analysis is the problem of deleting a minimum number of tuples from the input tables to make a given Boolean query false, which we refer to as " the resilience of a query. " In this paper, we study the complexity of resilience for self-join-free conjunctive queries with arbitrary functional dependencies. The cornerstone of our work is the novel concept of triads, a simple structural property of a query that leads to the several dichotomy results we show in this paper. The concepts of triads and resilience bridge the connections between the problems of deletion propagation and causal responsibility, and allow us to substantially advance the known complexity results in these topics. Specifically, we show a dichotomy for the complexity of resilience, which identifies previously unknown tractable families for deletion propagation with source side-effects, and we extend this result to account for functional dependencies. Further, we identify a mistake in a previous dichotomy for causal responsibility, and offer a revised characterization based purely on the structural form of the query (presence or absence of triads). Finally, we extend the dichotomy for causal responsibility in two ways: (a) we account for functional dependencies in the input tables, and (b) we compute responsibility for sets of tuples specified via wildcards.