In order to establish a mesh network, an electronic device may iteratively identify one or more mesh-network nodes and may determine associated duty-cycle ratios based on communication with the one or more mesh-network nodes. In particular, the electronic device may select candidate mesh-network nodes based on estimated throughput metrics of their communication with a root device in the mesh network. Then, for each of the candidate mesh-network nodes, the electronic device may associate with a given candidate mesh-network node, and may measure the throughput of the given candidate mesh-network node during a time interval by communicating packets. Based on comparisons of the measured throughputs, the electronic device may identify the one or more mesh-network nodes in the candidate mesh-network nodes and may determine the associated duty-cycle ratios. Subsequently, the electronic device communicates information with the root device via the one or more mesh-network nodes based on the duty-cycle ratios.