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We consider the traffic-aware channel assignment problem in a multi-radio Wireless Mesh Network that involves assigning channels to radio interfaces to optimize the performance of a set of TCP flows (flow throughput and fairness). The resulting optimization problem is NP-hard. At the TCP flow level, rapid traffic fluctuations are expected, imposing the need for frequent channel re-assignment to adapt to current traffic conditions. We develop a centralized greedy channel assignment algorithm suited for this task that can support frequent channel re-assignment by two properties: (i) low computational complexity, permitting it to quickly calculate a solution, and (ii) by taking into account the previous channel assignment to generate a new one with minimum variation. Focusing on the gateway access scenario, we observe an important benefit to optimizing the performance of TCP flows with the proposed algorithm.