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The wireless relay mesh network (WRMN) is designed to provide robust and fault tolerant communications between relay and user nodes in broadband wireless networks. In this paper, we study interference aware resource allocation in OFDMA based WRMNs and the effects of spatial reuse on throughput. We propose an interference aware subcarrier assignment (IASA) algorithm to allocate subcarriers to links in the network such that interference is mitigated and throughput is maximized. The protocol interference model and spatial reuse are exploited to achieve the subcarrier assignment. We show that our IASA algorithm improves throughput compared to when subcarriers are used only once. However, overuse of a single subcarrier can have detrimental effects on network performance, therefore a balance must be achieved. In addition, using a maximum concurrent flow (MCF) approach, we show that under the IASA scheme of spatial reuse, throughput can be enhanced. We formulate the MCF as a linear program and solve it using dual optimization techniques. We compare our proposed algorithm with that of a graph coloring approach using a conflict graph and column generation to show that our throughput results are better than those obtained by the link coloring strategy.