This paper proposes a theoretical model-driven channel assignment scheme designed to enhance network performance in multi-radio multi-channel wireless mesh networks. Unlike previous conflict graph-based channel assignments that addressed co-channel interference and hidden terminal problems while overlooking an exposed terminal problem, our proposed approach integrates these problems comprehensively to mitigate network performance degradation. Given a communication graph, we establish a conflict graph based on hop distance for practical implementation. The weighted conflict graph is constructed by analyzing packet collision conditions under the IEEE 802.11 standard with the CSMA/CA protocol, considering not only the transmission range and interference range but also the carrier sensing range simultaneously. Given a weighted conflict graph and available channel lists on each router, we devise a Weighted Soft List Coloring problem to address the channel assignment challenge. We prove the NP-hardness of this problem by establishing its dual problem, Max list-Cut. We present an approximation algorithm with worst-case performance at most twice the optimal solution while preserving network topology. We substantiate the performance of the proposed channel assignment algorithm through simulations in various topologies. The proposed algorithm, on average, demonstrates a network throughput increase of 162% and 174% compared to the greedy heuristic algorithm with 3 channels and 12 channels, respectively. ⓒ 2024 The Authors. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. For more information, see https://creativecommons.org/licenses/by-nc-nd/4.0/
