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

2025-07-18

AI Summary

This paper investigates the tractability of semiring aggregate conjunctive queries with GROUP-BY projections (e.g., AJAR/FAQ). Addressing the limitation of existing free-connex decompositions—which fail to capture the complexity of projection-aware aggregation—we introduce **project-connex treewidth**, a novel structural parameter, along with its associated project-connex tree decomposition. This framework uniformly characterizes tractability for enumeration, counting, and semiring aggregation of conjunctive queries. Building upon it, we devise a generic evaluation algorithm that integrates semiring algebraic semantics with syntactic query structure. We prove that when project-connex treewidth is bounded, query results can be enumerated with constant delay or counted in polynomial time. Moreover, the required decomposition is constructible efficiently via classical tree decomposition algorithms.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Data Mining & Knowledge Management: Intelligent Query Processing
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Semantics and Knowledge: Provenance, trust, security and privacy, and ethical issues in managing semantic data
• Search and Retrieval-Augmented AI: Agentic search

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.

Problem

• Measure tractability of aggregate group-by conjunctive queries
• Unify complexity bounds for semiring aggregate queries
• Extend free-connex decompositions for query evaluation

Innovation

• Introduces project-connex tree-width for tractability
• Unifies algorithmic manipulation for aggregate queries
• Links to classical tree decomposition algorithms