A Characterization of the Complexity of Resilience and Responsibility for Self-join-free Conjunctive Queries

TL;DR

This paper analyzes the computational complexity of the resilience problem for self-join-free conjunctive queries, establishing a complete dichotomy and exploring its relation to causal responsibility, with extensions to functional dependencies and wildcard tuple sets.

Contribution

It provides a complete complexity classification for resilience with functional dependencies, clarifies its relation to causal responsibility, and corrects previous dichotomies with broader applicability.

Findings

Resilience has a broader class of tractable queries than responsibility.

A complete dichotomy for resilience with functional dependencies is established.

A correction and extension of the causal responsibility dichotomy are presented.

Abstract

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. These applications usually rely on understanding how interventions in a database impact the output of a query. 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. We refer to this problem as "the resilience of a query" and show its connections to the well-studied problems of deletion propagation and causal responsibility. In this paper, we study the complexity of resilience for self-join-free conjunctive queries, and also make several contributions to previous known results for the problems of deletion propagation with source side-effects and causal responsibility: (1) We define the notion of resilience and provide a complete dichotomy for the class of self-join-free conjunctive queries with arbitrary functional dependencies; this dichotomy also extends and generalizes previous tractability results on deletion propagation with source side-effects. (2) We formalize the connection between resilience and causal responsibility, and show that resilience has a larger class of tractable queries than responsibility. (3) We identify a mistake in a previous dichotomy for the problem of causal responsibility and offer a revised characterization based on new, simpler, and more intuitive notions. (4) Finally, we extend the dichotomy for causal responsibility in two ways: (a) we treat cases where the input tables contain functional dependencies, and (b) we compute responsibility for a set of tuples specified via wildcards.