Scalable Optimal Transport Algorithm for Network Alignment

2026-07-11

AI Summary

This work addresses the scalability limitations of existing optimal transport–based network alignment methods, which suffer from frequent construction and updating of dense matrices. The authors propose FastAlign, a framework that preserves the original optimal transport formulation while reorganizing computations into hybrid sparse-dense operations through sparsity-aware graph processing, custom sparse matrix-matrix multiplication (SpMM) kernels, and kernel fusion techniques. FastAlign is the first approach to fully exploit sparsity without altering the underlying model, achieving speedups of 2.24×–9.45× on CPU and 2.24×–32.54× on GPU compared to prior methods, while maintaining alignment accuracy on par with state-of-the-art approaches.

Abstract

Network alignment identifies node correspondences across different networks and is a fundamental primitive in many data science applications, including social network analysis, fraud detection, and knowledge graph integration. However, state-of-the-art network alignment methods often achieve high accuracy by repeatedly constructing and updating dense matrices, sacrificing scalability in the process. To address this scalability limitation without compromising alignment accuracy, we present FastAlign, a scalable, sparsity-aware framework for optimal transport-based network alignment. Rather than introducing a new alignment model, FastAlign preserves the original OT formulation and reinterprets its computation as a set of recurring mixed sparse-dense operations. FastAlign combines sparsity-aware graph computation with domain-specific kernel fusion, including a custom SpMM kernel. Our results show that FastAlign achieves alignment quality comparable to state-of-the-art OT-based methods while substantially reducing end-to-end runtime up to 3.89x-9.45x on CPU and 2.24x-32.54x on GPU.

Problem

• network alignment
• optimal transport
• scalability
• sparsity
• dense matrices

Innovation

• optimal transport
• network alignment
• sparsity-aware computation
• kernel fusion
• SpMM