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To create a wireless backbone network, channel allocation algorithms in mesh networks have been actively researched these days, but they still have the problem of scalability. When they operate in a centralized manner, they are not able to guarantee the upper-bound of the channel allocation time. This paper considers a new channel allocation algorithm that works under the environments of directional antennas. It allocates channels in a distributed manner and also adaptively by reflecting the traffic demand. To do so, we reconstruct the network into several groups to apply 2P MAC protocol, remove the interference caused by the directional antennas, and allocate a channel to each link without resorting to a central manager. Through simulation work, we prove that our distributed and adaptive channel allocation (DACA) achieves good performance, in terms of packet drop and channel allocation delay, compared with the other competitive channel allocation algorithms.