Let's Play Tag: Linear Time Evaluation of Conjunctive Queries under TGD Constraints

2026-03-19

AI Summary

This study investigates whether conjunctive queries can be evaluated in linear time under tuple-generating dependencies (TGDs) across multiple evaluation modes, including single-test, all-test, counting, and lexicographic direct access. It extends the well-known complexity dichotomy for unconstrained conjunctive queries to settings with TGDs, focusing on two classes: non-recursive TGDs whose head relation symbols are at most binary (or whose frontier variables number at most two), and full frontier-guarded TGDs. By integrating syntactic properties of TGDs, logical modeling, and algorithmic design, the work establishes linear-time solvability for all evaluation modes except enumeration. Furthermore, it identifies fundamental theoretical barriers that prevent similar tractability results for query enumeration and broader classes of TGDs.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

We study the limits of linear time evaluation of conjunctive queries under constraints expressed as tuple-generating dependencies (TGDs), across several modes of query evaluation: single-testing, all-testing, counting, lexicographic direct access, and enumeration. While full classifications seem far beyond reach, we propose an approach that, for some evaluation modes and classes of TGDs, makes it possible to lift known dichotomies from the unconstrained setting. In particular, our approach applies to all mentioned evaluation modes except enumeration, when the constraints fall into one of two classes: non-recursive sets of TGDs in which every TGD uses at most binary relation symbols in the head or has at most two frontier variables; and frontier-guarded full TGDs. We further provide a collection of examples showcasing the challenges that arise for enumeration and for less restrictive classes of TGDs.

Problem

• conjunctive queries
• tuple-generating dependencies
• linear time evaluation
• query enumeration
• frontier variables

Innovation

• conjunctive queries
• tuple-generating dependencies
• linear time evaluation
• dichotomy lifting
• frontier-guarded TGDs