Efficient Minimum Weight Vertex Cover Heuristics Using Graph Neural Networks

Abstract

Minimum weighted vertex cover is the NP-hard graph problem of choosing a subset of vertices incident to all edges such that the sum of the weights of the chosen vertices is minimum. Previous efforts for solving this in practice have typically been based on search-based iterative heuristics or exact algorithms that rely on reduction rules and branching techniques. Although exact methods have shown success in solving instances with up to millions of vertices efficiently, they are limited in practice due to the NP-hardness of the problem. We present a new hybrid method that combines elements from exact methods, iterative search, and graph neural networks (GNNs). More specifically, we first compute a greedy solution using reduction rules whenever possible. If no such rule applies, we consult a GNN model that selects a vertex that is likely to be in or out of the solution, potentially opening up for further reductions. Finally, we use an improved local search strategy to enhance the solution further. Extensive experiments on graphs of up to a billion edges show that the proposed GNN-based approach finds better solutions than existing heuristics. Compared to exact solvers, the method produced solutions that are, on average, 0.04% away from the optimum while taking less time than all state-of-the-art alternatives. based on Dataset 1 and 3, we present a deeper analysis of the different components of our GNN-based approach. Finally, we include results on Dataset 4.