Maximum Independent Set: Self-Training through Dynamic Programming

Lorenzo Brusca, Lars C.P.M. Quaedvlieg, Stratis Skoulakis, Grigorios Chrysos, Volkan Cevher

Keywords: Maximum Independent Set, Combinatorial Optimization, Graph Neural Networks, Dynamic Programming

TL;DR: We propose a neural approach that is inspired by dynamic programming to tackle the Maximum Independent Set problem

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.

Submission Number: 8295