$Δ$-Motif: Parallel Subgraph Isomorphism via Tabular Operations for Scalable Layout Selection

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 $595\times$ 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.