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We consider the problem of scheduling packets transmission across the switching fabric in an input-queued switch. In order to achieve maximum throughput, scheduling algorithms usually employ the queue length as a parameter for determining the priority to serve a given queue. Unfortunately, optimal schedulers are too complex to be implemented directly in hardware, which is the only viable solution in high-end switches, since scheduling decisions must be taken in very short time, of order of ns. Conversely, implementable algorithms, based on parallel and greedy decisions, are inefficient in terms of throughput. In this work we do not propose any new scheduling algorithm or switching architecture, but a novel scheme to optimize the performance of a pre-existing scheduler. Indeed, we propose to assist the scheduling decision by considering "message" values instead of queue lengths. Such messages are obtained by running an iterative parallel algorithm (efficiently implementable in hardware and fully compatible with pre-existing schedulers), based on a rigorous Belief-Propagation approach. We show that BP-assisted scheduling is able to boost the performance of a given scheduler, reaching almost optimal throughput, even under critical traffic scenarios.