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Topology control is one of the important techniques in wireless multi-hop networks to preserve connectivity and extend the network lifetime. This is more significant in ZigBee, since the address assignment scheme is tightly coupled with topology construction. For example, there can be orphan nodes that cannot receive the network address and isolated from the network due to predefined network configurations. In this paper, we propose a distributed topology construction algorithm that controls the association time of each node in order to solve the orphan node problem in ZigBee as well as construct an efficient routing tree topology. The main idea of the distributed topology construction algorithm is to construct primary backbone nodes by propagating the invitation packets and controlling the association time based on the link quality. Since the dynamically selected primary nodes are spread throughout the network, they can provide backbone to accept the association requests from the remaining secondary nodes which are majority in a network. In the performance evaluation, we show that the proposed topology construction algorithm effectively solves the orphan node problem regardless of network density as well as provides efficient tree routing cost comparable to the approximation algorithm for degree constrained minimum routing cost tree (DC-MRCT) problem. [ABSTRACT FROM AUTHOR]