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A topology-transparent scheduling algorithm is created without requiring changes to existing schedules when network topology changes in highly volatile mobile networks. It uses only the maximum number and degree of nodes of the network, therefore no changes are required to existing schedules. However, it is often difficult to estimate a priori the maximum nodal degree. Also, the nodal degree may vary significantly within the network. In this paper, we present a threaded topology-transparent scheduling protocol that is composed of a throughput optimal topology-transparent scheduling algorithm. While maintaining the advantages of the component algorithm, it does not rely on the maximum nodal degree.