Unsupervised Learning of Local Updates for Maximum Independent Set in Dynamic Graphs

TL;DR

This paper introduces an unsupervised learning model using graph neural networks for efficiently approximating maximum independent sets in dynamic graphs, outperforming some existing models in speed and size of solutions.

Contribution

It presents the first unsupervised, update-based neural approach for MaxIS in dynamic graphs, combining structural learning with a distributed update mechanism.

Findings

Achieves competitive approximation ratios on dynamic graphs of 200-1,000 nodes.

Runs 1.91-6.70x faster than a mixed integer programming solver.

Generalizes to larger graphs, producing larger MaxIS solutions than other unsupervised models.

Abstract

We present the first unsupervised learning model for Maximum-Independent-Set (MaxIS) in dynamic graphs where edges change over time. Our method combines structural learning from graph neural networks (GNNs) with a learned distributed update mechanism that, given an edge addition or deletion event, modifies nodes' internal memories and infers their MaxIS membership in a single, parallel step. We evaluate our model against a mixed integer programming solver and a breadth of unsupervised and supervised learning models for combinatorial optimization on static graphs. Across dynamic graphs of 200-1,000 nodes, our model achieves approximation ratios that are competitive with the state-of-the-art models while running 1.91-6.70x faster. When generalizing to graphs with 100x more nodes than those used for training, our model produces MaxIS solutions 1.00-1.18x larger than all other unsupervised models, but is outperformed by the state-of-the-art supervised model. These results demonstrate that this novel, unsupervised, update-based learning approach to dynamic combinatorial optimization is a viable alternative to the na\"ive reapplication of analogous models for static graphs, leveraging temporal information to improve neural methods for combinatorial optimization.