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In a wireless mesh network (WMN), mesh routers (MRs) are interconnected by wireless links and form a wireless backbone to provide ubiquitous high-speed Internet connectivity for mobile clients (MCs). The wireless backbone is tightly integrated with the Internet by a special kind of nodes called as Internet gateways (IGWs). Even though the capacity of WMN can be improved by equipping the MRs with multiple radios working at non-overlapping channels, the deployment of IGW is critical to the network performance of WMN. In this paper, we address the IGW placement problem based on a hierarchical cluster based architecture. The problem is first formulated as a linear program (LP) issue, then some heuristic algorithms are developed. Our simulation results show the effectiveness of the proposed algorithms.