Minimal-Change Integrity Maintenance Using Tuple Deletions

TL;DR

This paper investigates the computational complexity of maintaining database integrity through minimal tuple deletions, analyzing repair checking and consistent query answering across various constraints.

Contribution

It provides a complexity classification for integrity maintenance problems, identifying tractable and intractable cases for different types of constraints.

Findings

Identifies tractable cases for repair checking and query answering.

Shows intractability results for certain constraints, highlighting limitations.

Provides insights for practical implementation of integrity enforcement mechanisms.

Abstract

We address the problem of minimal-change integrity maintenance in the context of integrity constraints in relational databases. We assume that integrity-restoration actions are limited to tuple deletions. We identify two basic computational issues: repair checking (is a database instance a repair of a given database?) and consistent query answers (is a tuple an answer to a given query in every repair of a given database?). We study the computational complexity of both problems, delineating the boundary between the tractable and the intractable. We consider denial constraints, general functional and inclusion dependencies, as well as key and foreign key constraints. Our results shed light on the computational feasibility of minimal-change integrity maintenance. The tractable cases should lead to practical implementations. The intractability results highlight the inherent limitations of any integrity enforcement mechanism, e.g., triggers or referential constraint actions, as a way of performing minimal-change integrity maintenance.