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Smart Home Wireless Mesh Networks (SH-WMNs) have emerged to become one of the promising applications of Wireless Sensor Networks (WSNs). In SH-WMNs, con- nected dominating set (CDS) is one of candidates for clus- tering formation or virtual backbone construction. During the CDS construction, however, the link that has enough bandwidth to support more end-devices should be selected in order to enhance overall network throughput and relia- bility. Our LQ-CDS construction scheme can improve the network performance via two metrics: interference metric and bandwidth metric. The simulation results show that LQ-CDS constructs the virtual backbone with the small sub- set of DS and the link that has better bandwidth.