Learning-Based Heuristic for Combinatorial Optimization of the Minimum Dominating Set Problem using Graph Convolutional Networks

A dominating set of a graph $\mathcal{G=(V, E)}$ is a subset of vertices $S\subseteq\mathcal{V}$ such that every vertex $v\in \mathcal{V} \setminus S$ outside the dominating set is adjacent to a vertex $u\in S$ within the set. The minimum dominating set problem seeks to find a dominating set of minimum cardinality and is a well-established NP-hard combinatorial optimization problem. We propose a novel learning-based heuristic approach to compute solutions for the minimum dominating set problem using graph convolutional networks. We conduct an extensive experimental evaluation of the proposed method on a combination of randomly generated graphs and real-world graph datasets. Our results indicate that the proposed learning-based approach can outperform a classical greedy approximation algorithm. Furthermore, we demonstrate the generalization capability of the graph convolutional network across datasets and its ability to scale to graphs of higher order than those on which it was trained. Finally, we utilize the proposed learning-based heuristic in an iterative greedy algorithm, achieving state-of-the-art performance in the computation of dominating sets.