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Since Wireless Mesh Networks (WMNs) can be easily deployed without wirelines among wireless mesh routers, they allow us to quickly recover network access services in disaster areas even if the existing network infrastructures have been enormously destroyed by terrible earthquake, tsunami, and so on. However, the performance of wireless mesh networks is largely affected by many factors, e.g., wireless mesh routers' locations, channel assignment, transmission scheduling, etc. In particular, the method of selecting gateways which has a connection to external networks significantly impacts on the network performance when the topology and routing have been fixed in the wireless mesh network. In this paper, we suppose a wireless mesh network which consists of wireless mesh routers and a base station directly connected to external networks. The base station is located at the center of the wireless mesh network chooses a certain number of wireless mesh routers as gateways, and establishes a connection with each of them. Our goal is to easily and quickly find the candidate gateways that maximize the system throughput without solving a complex optimization problem which includes a large number of parameters and involves heavy computation load. The performance of the proposed scheme is evaluated by numerical analysis, and demonstrated through computer simulations. The results show that our proposed scheme can determine the appropriate candidate gateway with high accuracy when there is a certain variance in the amount of traffic generated by users at each wireless mesh router.