$Δ$-Motif: Subgraph Isomorphism at Scale via Data-Centric

2025-08-28

AI Summary

Subgraph isomorphism—a fundamental NP-complete graph analysis problem—is critical in biological network analysis, social mining, and quantum circuit optimization. However, classical backtracking algorithms (e.g., VF2) suffer from severe sequential bottlenecks, limiting their scalability on modern parallel hardware. This paper introduces the first relational-database formulation of subgraph isomorphism, proposing a computation paradigm based on motif decomposition and scalable joins. By reformulating graph structures as relational tables, our approach leverages highly optimized, parallel join, filter, and merge operations from the RAPIDS/Pandas ecosystem to achieve GPU acceleration—without requiring low-level programming. The method supports cross-platform parallel execution and delivers up to 595× speedup over VF2 on large-scale graphs. We further demonstrate its practical impact by integrating it into quantum circuit compilation, significantly enhancing real-world scalability.

Technology Category

• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery 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
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

Subgraph isomorphism is a fundamental problem in graph analysis that seeks to find all instances of a pattern graph within a larger data graph while preserving structural relationships. This NP-complete problem is central to domains such as biological network analysis, social network mining, and quantum circuit optimization. Traditional approaches rely on backtracking algorithms like VF2, which suffer from sequential bottlenecks that limit their ability to exploit modern parallel hardware. In this work, we introduce $Δ$-Motif, a GPU-accelerated subgraph isomorphism algorithm that reformulates the task through the lens of database operations. Our key insight is to represent both data and pattern graphs in tabular form, turning subgraph isomorphism into database primitives including joins, sorts, merges, and filters. $Δ$-Motif decomposes graphs into small building blocks called motifs and systematically combines them using scalable relational operations. By leveraging mature, optimized libraries from the NVIDIA RAPIDS ecosystem and Pandas framework, our solution achieves massive parallelism while remaining portable across systems supporting standard relational primitives. Benchmarks show that $Δ$-Motif outperforms established algorithms like VF2, achieving speedups of up to $595 imes$ on GPUs. We further demonstrate its impact by applying it to quantum circuit compilation, addressing a critical bottleneck in quantum computing and enabling scaling to near- and medium-term devices. Our approach democratizes high-performance graph processing by exposing it through familiar database abstractions, eliminating the need for low-level programming while delivering exceptional computational efficiency.

Problem

• Accelerating subgraph isomorphism for large-scale graph analysis
• Overcoming sequential bottlenecks in traditional backtracking algorithms
• Enabling GPU-accelerated pattern matching through database operations

Innovation

• GPU-accelerated subgraph isomorphism algorithm
• Represents graphs as tabular database primitives
• Leverages RAPIDS and Pandas for massive parallelism