Combining Relational Algebra, SQL, Constraint Modelling, and Local Search

TL;DR

This paper introduces non-deterministic extensions to relational algebra and SQL with constraint modeling capabilities, enabling the expression of NP problems, and demonstrates their effectiveness through implementation and examples.

Contribution

It proposes novel non-deterministic query language extensions with constraint modeling, enhancing expressiveness for combinatorial problems in relational databases.

Findings

Extensions can express all NP problems

Syntactical restrictions achieve polynomial data complexity

Implementation using local search techniques demonstrates practicality

Abstract

The goal of this paper is to provide a strong integration between constraint modelling and relational DBMSs. To this end we propose extensions of standard query languages such as relational algebra and SQL, by adding constraint modelling capabilities to them. In particular, we propose non-deterministic extensions of both languages, which are specially suited for combinatorial problems. Non-determinism is introduced by means of a guessing operator, which declares a set of relations to have an arbitrary extension. This new operator results in languages with higher expressive power, able to express all problems in the complexity class NP. Some syntactical restrictions which make data complexity polynomial are shown. The effectiveness of both extensions is demonstrated by means of several examples. The current implementation, written in Java using local search techniques, is described. To appear in Theory and Practice of Logic Programming (TPLP)