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In a wireless mesh network, an efficient utilization of multiple radios with multiple channels involves the assignment of channels to radios/links. This becomes an optimization problem for which various objectives can be defined with various conflicting constraints and requirements. We present a novel channel assignment strategy based on predicted upper-bound and lower-bound of interference associated with particular assignments. An additional design is also proposed to prevent the possibility that two ends of any designated link are not assigned a common channel. Simulation results indicate that the proposed algorithm outperforms existing approaches in the number of operative links when only few channels or sufficiently many radios are provided.