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Radio spectrum scarcity hampers the development of new wireless technologies and services. Cognitive radios have been proposed to enable unlicensed (or secondary) users to borrow locally idle bands of the spectrum provided that no significant interference is created for the licensed (or primary) users. Fast adaptation to the changing spectrum availability is naturally a major requirement in such systems. This adaptation consists of detecting the spectrum occupied by the primary users, computing a new resource allocation for the secondary network, and communicating this allocation through the network. In that context, we develop a resource allocation scheme for multi-input-multi-output wireless mesh networks. The proposed algorithm combines low computational complexity and light control traffic thanks to a combination of relevant approximations in the general nonpolynomial-hard allocation problem. The allocation consists of two steps. First, a centralized carrier allocation is performed at a coordinator node based on partial knowledge of the network parameters. Then, each node locally computes its power allocation through simple water-filling algorithms. Numerical results show that compared to state-of-the-art techniques, 10% of the total throughput of the network is sacrificed to reduce the computation time and the control traffic by two orders of magnitude.