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In this work, we consider a distributed link-weighted and distance-constrained channel assignment (DLDCA) algorithm for a multi-channel multi-hop mesh network, such as community wireless networks, to maximize its throughput. Efficient channel assignment could greatly reduce interference of each link from its neighboring links and subsequently improve the network throughput. In response to it, we introduce an interference metric, namely, Min-Max I-value of an edge (MMIE), to explicitly accounts for interference among links that are at distance one. In addition, we further show that the above problem with respect to MMIE is NP-hard in computation. This guides us to develop a new distributed channel assignment algorithm called DLDCA algorithm. We study the DLDCA performance by implementing it in a wireless simulation environment. The simulation results show that in a multi-channel multi-hop network, DLDCA significantly outperforms previously proposed channel assignment schemes.