We consider the problem of scheduling the transmission of packets 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. In this work, we propose a novel scheme to optimize the performance of a preexisting scheduler. Our main idea is to assist the scheduling decision, considering "messagesâ rather than queue lengths. Such messages are obtained by running an iterative parallel algorithm, inspired by a rigorous belief-propagation approach. We demonstrate that belief-propagation-assisted scheduling is able to boost the performance of a given scheduler, reaching almost optimal throughput, even under critical traffic scenarios.