Maximum Independent Set: Self-Training through Dynamic Programming
This work addresses a fundamental combinatorial optimization problem in graph theory, with potential applications in network design and scheduling, but appears incremental as it builds on existing GNN and DP techniques.
The authors tackled the maximum independent set problem by developing a graph neural network framework inspired by dynamic programming, which uses a self-training process to improve accuracy. Their method outperformed prior approaches on synthetic and real-world datasets, though no specific numerical gains were provided in the abstract.
This work presents a graph neural network (GNN) framework for solving the maximum independent set (MIS) problem, inspired by dynamic programming (DP). Specifically, given a graph, we propose a DP-like recursive algorithm based on GNNs that firstly constructs two smaller sub-graphs, predicts the one with the larger MIS, and then uses it in the next recursive call. To train our algorithm, we require annotated comparisons of different graphs concerning their MIS size. Annotating the comparisons with the output of our algorithm leads to a self-training process that results in more accurate self-annotation of the comparisons and vice versa. We provide numerical evidence showing the superiority of our method vs prior methods in multiple synthetic and real-world datasets.