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The network throughput of a Wireless Mesh Network (WMN) can be improved by utilizing multiple channels, multiple radio interfaces and directional antenna technology. When the numbers of available channels and radio interfaces in a WMN system are constant, efficient time scheduling among links is essential to avoid potential interference and conflict. In this paper, we assume a WMN with multiple gateway nodes and each node is equipped with multiple radio interfaces and directional antenna. First, we propose an algorithm to divide scheduling procedure into several steps according to maximal independent sets in interference and conflict graph. Then we construct a linear program model to capture the end-to-end throughputs of source-destination pairs and link scheduling matrix which describe the active time fraction of each link in each scheduling step, and the minimum scheduled end-to-end throughput is maximized. The obtained link scheduling matrix may not make all the end-to-end throughputs achieve upper bounds. Thus we propose an algorithm to improve the link scheduling matrix to make all the end-to-end throughputs achieve upper bounds. Finally, we compared the proposed link scheduling algorithm with other link scheduling algorithms, and the numerical result shows performance of our proposed algorithm is much better.