Efficient scheduling of transmissions is a key problem in wireless networks. The main challenge stems from the fact that optimal link scheduling involves solving a maximum weighted independent set (MWIS) problem, which is known to be NP-hard. For practical link scheduling schemes, centralized and distributed greedy heuristics are commonly used to approximate the solution to the MWIS problem. However, these greedy schemes mostly ignore important topological information of the wireless network. To overcome this limitation, we propose fast heuristics based on graph convolutional networks (GCNs) that can be implemented in centralized and distributed manners. Our centralized MWIS solver is based on tree search guided by a trainable GCN module and 1-step rollout. In our distributed MWIS solver, a trainable GCN module learns topology-aware node embeddings that are combined with the network weights before calling a distributed greedy solver. Test results on medium-sized wireless networks show that a GCN-based centralized MWIS solver can reach a near-optimal solution quickly. Moreover, we demonstrate that a shallow GCN-based distributed MWIS scheduler can reduce by nearly half the suboptimality gap of the distributed greedy solver with minimal increase in complexity. The proposed scheduling solutions also exhibit good generalizability across graph and weight distributions.
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