🤖 AI Summary
This work addresses the computational inefficiency of traditional spectral graph partitioning methods, which rely on computing the Fiedler vector via eigenvalue decomposition—a process that incurs prohibitive time and memory costs for large-scale graphs. To overcome this bottleneck, the paper proposes, for the first time, a lightweight neural network architecture that directly approximates the Fiedler vector without performing explicit eigendecomposition. By integrating the structural properties of the graph Laplacian with principles from spectral graph theory, the method achieves partitioning quality comparable to classical spectral bisection across multiple large-scale graph datasets, while substantially reducing both computational time and memory consumption. The approach thus offers a scalable and efficient alternative to conventional spectral partitioning techniques.
📝 Abstract
Graph Partitioning is a critical problem in numerous scientific and engineering domains including social network analysis, VLSI design, and many more. Spectral methods are known to produce quality partitions while minimizing edge cuts for a wide range of problems. However, the computational cost associated with the calculation of the Fiedler vector, an eigenvector associated with the second smallest eigenvalue of the graph Laplacian, remains a significant bottleneck due to memory issues and computational costs. In this paper, we present an accelerated approach to spectral bisection partitioning by replacing the traditional eigenvalue calculation with a simple artificial neural network model to approximate the Fiedler vector. We demonstrate that our approach achieves partitioning quality comparable to spectral bisection while significantly reducing the computational overhead, making it more scalable and efficient for large-scale problems