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The IEEE 802.16 standard recently introduced an additional relay mode of operation permitting coverage extension of the point-to-multipoint (PMP) based WiMAX networks. Relays can further aid in increasing the achievable data rates for subscriber stations (SS) in the network. Although bandwidth management and scheduling have been studied in some detail in traditional IEEE 802.16 PMP networks, the corresponding study for relay networks is far from complete. A trivial extension to the scheduling and bandwidth allocation algorithms used in the PMP mode for the relay networks leads to inefficient bandwidth utilization and allocation. Of particular interest here is the possibility of spatial reuse of allocated blocks of bandwidth which is permissible in relay networks. This paper investigates and designs bandwidth allocation and scheduling algorithms for IEEE 802.16 based relay networks, considering the support for spatial reuse to additionally improve the throughput while at the same time supporting quality of service (QoS). We research the issues which need to be considered when designing bandwidth allocation algorithms for relay networks. Finally, as a proof of concept we provide a thorough simulation study to investigate the performance of the designed algorithms. The results validate the design choices we presented, and also provide insights into areas for further research in WiMAX relay networks.