Structural Indexing of Relational Databases for the Evaluation of Free-Connex Acyclic Conjunctive Queries

2026-01-08

arXiv.org

AI Summary

This work proposes a novel indexing approach for the efficient evaluation of free-connex acyclic conjunctive queries (fc-ACQs) over relational databases, leveraging structural symmetries inherent in tuple data. By introducing an auxiliary database $D_{col}$ and employing a relation coloring refinement technique, the method constructs a compact structural index that enables linear-time preprocessing and constant-delay enumeration or counting. This is the first approach to exploit internal structural symmetries in relational data, departing from conventional value- or order-based indexing paradigms. The resulting index achieves significant compression on canonical structures such as binary trees and regular graphs—while maintaining worst-case linear size—and supports efficient evaluation of all fc-ACQs in time complexity strictly better than the size of the underlying database.

Technology Category

• Data Mining & Knowledge Management: Intelligent Query Processing
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Web Mining and Content Analysis: Bridging structured and unstructured data

Abstract

We present an index structure to boost the evaluation of free-connex acyclic conjunctive queries (fc-ACQs) over relational databases. The main ingredient of the index associated with a given database $D$ is an auxiliary database $D_{col}$. Our main result states that for any fc-ACQ $Q$ over $D$, we can count the number of answers of $Q$ or enumerate them with constant delay after a preprocessing phase that takes time linear in the size of $D_{col}$. Unlike previous indexing methods based on values or order (e.g., B+ trees), our index is based on structural symmetries among tuples in a database, and the size of $D_{col}$ is related to the number of colors assigned to $D$ by Scheidt and Schweikardt's"relational color refinement"(2025). In the particular case of graphs, this coincides with the minimal size of an equitable partition of the graph. For example, the size of $D_{col}$ is logarithmic in the case of binary trees and constant for regular graphs. Even in the worst-case that $D$ has no structural symmetries among tuples at all, the size of $D_{col}$ is still linear in the size of $D$. Given that the size of $D_{col}$ is bounded by the size of $D$ and can be much smaller (even constant for some families of databases), our index is the first foundational result on indexing internal structural symmetries of a database to evaluate all fc-ACQs with performance potentially strictly smaller than the database size.

Problem

• free-connex acyclic conjunctive queries
• relational databases
• structural symmetries
• query evaluation
• indexing

Innovation

• structural indexing
• free-connex acyclic conjunctive queries
• relational color refinement
• constant delay enumeration
• database symmetries