Stop the Chase

TL;DR

This paper introduces a new, efficiently checkable condition called inductive restriction that guarantees chase termination in databases, and explores data-dependent conditions that can ensure termination for specific instances.

Contribution

It proposes a novel sufficient termination condition called inductive restriction that generalizes previous conditions and can be efficiently verified, along with data-dependent conditions for fixed instances.

Findings

Inductive restriction strictly generalizes previous chase termination conditions.

Data-dependent conditions can guarantee chase termination for specific database instances.

The proposed conditions are more broadly applicable and efficiently checkable.

Abstract

The chase procedure, an algorithm proposed 25+ years ago to fix constraint violations in database instances, has been successfully applied in a variety of contexts, such as query optimization, data exchange, and data integration. Its practicability, however, is limited by the fact that - for an arbitrary set of constraints - it might not terminate; even worse, chase termination is an undecidable problem in general. In response, the database community has proposed sufficient restrictions on top of the constraints that guarantee chase termination on any database instance. In this paper, we propose a novel sufficient termination condition, called inductive restriction, which strictly generalizes previous conditions, but can be checked as efficiently. Furthermore, we motivate and study the problem of data-dependent chase termination and, as a key result, present sufficient termination conditions w.r.t. fixed instances. They are strictly more general than inductive restriction and might guarantee termination although the chase does not terminate in the general case.