Path-based Algebraic Foundations of Graph Query Languages

TL;DR

This paper introduces an algebraic framework for evaluating path queries in graph databases, enabling formal analysis, implementation support, and optimization of path query languages like GQL and SQL/PGQ.

Contribution

It presents a novel abstract algebra for path queries, bridging standards and implementations, and facilitating query optimization and comparison.

Findings

Algebra can express core path query fragments of GQL and SQL/PGQ.

Evaluation trees serve as logical plans for query execution.

Framework supports query optimization techniques.

Abstract

Graph databases are gaining momentum thanks to the flexibility and expressiveness of their data models and query languages. A standardization activity driven by the ISO/IEC standardization body is also ongoing and has already conducted to the specification of the first versions of two standard graph query languages, namely SQL/PGQ and GQL, respectively in 2023 and 2024. Apart from the standards, there exists a panoply of concrete graph query languages provided by current graph database systems, each offering different query features. A common limitation of current graph query engines is the absence of an algebraic approach for evaluating path queries. To address this, we introduce an abstract algebra for evaluating path queries, allowing paths to be treated as first-class entities within the query processing pipeline. We demonstrate that our algebra can express a core fragment of path queries defined in GQL and SQL/PGQ, thereby serving as a formal framework for studying both standards and supporting their implementation in current graph database systems. We also show that evaluation trees for path algebra expressions can function as logical plans for evaluating path queries and enable the application of query optimization techniques. Our algebraic framework has the potential to act as a lingua franca for path query evaluation, enabling different implementations to be expressed and compared.