New Results for the Complexity of Resilience for Binary Conjunctive Queries with Self-Joins

Abstract

The resilience of a Boolean query 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 binary conjunctive queries with self-joins (i.e. conjunctive queries with relations of maximal arity 2) with one repeated relation. 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. Overall, we give a dichotomy result for the restricted setting when one relation is repeated at most 2 times, and we cover many of the cases for 3. 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.1 While some prior work on related problems does allow for self-joins [2,5,9], the complexity characterizations in those results are not specific to the queries, but rather to high-level operators (e.g, join, projection, etc.). In contrast, our work provides results that are fine-grained and identify elements of the query structure that render the resilience problem NP-complete or PTIME-computable.

Aggregated Deletion Propagation for Counting Conjunctive Query Answers

“…Finally, closely related to the ADP is the resilience problem, originally studied by Freire et al for the class of CQs without self-joins and functional dependencies [11] (see also [12] for an extension to a class of queries with self-joins). The input to the resilience problem is a Boolean CQ and a database D such that Q(D) is true, and the goal is to remove a minimum set of tuples from D to make Q false on D. Observe that the resilience problem is identical to ADP with k = |Q(D)|.…”