Project-connex Decompositions and Tractability of Aggregate Group-by Conjunctive Queries

TL;DR

This paper introduces 'project-connex' tree-width, a new measure that unifies and explains tractability results for aggregate conjunctive queries over semirings, enabling efficient evaluation and enumeration.

Contribution

It defines project-connex tree-width as a novel, elementary measure that extends known decompositions to unify tractability results for aggregate and conjunctive queries.

Findings

Unified framework for aggregate query evaluation

Recovery of known tractability results

Algorithms for computing project-connex decompositions

Abstract

We introduce 'project-connex' tree-width as a measure of tractability for counting and aggregate conjunctive queries over semirings with 'group-by' projection (also known as 'AJAR' or 'FAQ' queries). This elementary measure allows to obtain comparable complexity bounds to the ones obtained by previous structural conditions tailored for efficient evaluation of semiring aggregate queries, enumeration algorithms of conjunctive queries, and tractability of counting answers to conjunctive queries. Project-connex tree decompositions are defined as the natural extension of the known notion of 'free-connex' decompositions. They allow for a unified, simple and intuitive algorithmic manipulation for evaluation of aggregate queries and explain some existing tractability results on conjunctive query enumeration, counting conjunctive query evaluation, and evaluation of semiring aggregate queries. Using this measure we also recover results relating tractable classes of counting conjunctive queries and bounded free-connex tree-width, or the constant-time delay enumeration of semiring aggregate queries over bounded project-connex classes. We further show that project-connex tree decompositions can be obtained via algorithms for computing classical tree decompositions.