Foundations of the GraphAlg Language

2026-04-13

AI Summary

This work addresses the challenge of efficiently expressing and executing user-defined graph algorithms in graph databases by proposing a solution grounded in the formal matrix language MATLANG. The authors extend MATLANG to construct GraphAlg Core, serving as an intermediate representation for the graph algorithm language GraphAlg, and provide the first rigorous proof that its core fragment can be effectively simulated by for-MATLANG—an extension of MATLANG supporting synchronous iteration. This study establishes a formal theoretical connection between high-level graph algorithm languages and matrix-based computation, offering a solid foundation for compiling and executing graph algorithms within database systems. By doing so, it advances the practical adoption of domain-specific languages (DSLs) in graph processing and contributes to the formal underpinnings of graph query and algorithm evaluation.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Knowledge Representation and Reasoning: Knowledge Representation Languages
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic 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
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

The GraphAlg domain-specific language for graph algorithms enables user-defined algorithms in graph databases. In this work we show how GraphAlg is built on top of the formal MATLANG language for matrix manipulation. Starting from MATLANG, we describe the extensions to MATLANG needed to derive GraphAlg Core, a simplified version of GraphAlg that is used as the internal representation in the GraphAlg compiler. Furthermore, we prove that any GraphAlg Core expression can be simulated in an extension of for-MATLANG that supports simultaneous induction.

Problem

• GraphAlg
• MATLANG
• graph algorithms
• domain-specific language
• formal foundation

Innovation

• GraphAlg
• MATLANG
• domain-specific language
• matrix manipulation
• simultaneous induction