Deep Learning and Spectral Embedding for Graph Partitioning

TL;DR

This paper introduces a novel graph partitioning method using a graph neural network with a multilevel structure, achieving comparable quality to traditional algorithms but with faster runtime.

Contribution

The paper proposes a new GNN-based graph partitioning algorithm that integrates spectral theory and multilevel coarsening, improving scalability and efficiency.

Findings

Partition quality comparable to METIS and spectral methods

Shorter runtime than traditional spectral partitioning

Effective generalization to larger graphs

Abstract

We present a graph bisection and partitioning algorithm based on graph neural networks. For each node in the graph, the network outputs probabilities for each of the partitions. The graph neural network consists of two modules: an embedding phase and a partitioning phase. The embedding phase is trained first by minimizing a loss function inspired by spectral graph theory. The partitioning module is trained through a loss function that corresponds to the expected value of the normalized cut. Both parts of the neural network rely on SAGE convolutional layers and graph coarsening using heavy edge matching. The multilevel structure of the neural network is inspired by the multigrid algorithm. Our approach generalizes very well to bigger graphs and has partition quality comparable to METIS, Scotch and spectral partitioning, with shorter runtime compared to METIS and spectral partitioning.