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In this paper, we address the problem of determining an optimal topology for Bluetooth wireless personal area networks (BT-WPANs). In BT-WPANs, multiple communication channels are available, through a frequency hopping technique. The way network nodes are grouped to share the same channel, and which nodes are selected to bridge traffic from a channel to another, has a significant impact on the capacity and throughput of the system, as well as the nodes' battery lifetime. The determination of an optimal topology is thus extremely important. Our approach is based on a min-max formulation of the optimization problem, which produces topologies that minimize the traffic load of the most congested node in the network (thus also minimizing energy consumption) while meeting the traffic requirements and the constraints posed by the BT-WPAN technology. We investigate the performance of the topologies produced by our optimization approach as the system requirements vary, and evaluate the trade-offs existing between system complexity and network efficiency. Results show that a topology optimized for some traffic requirements is remarkably robust to changes in the traffic pattern. Due to the problem complexity, the optimal solution is attained in a centralized manner. Although this implies severe limitations, a centralized solution can be applied whenever a network coordinator is elected, and provides a useful term of comparison for any distributed heuristics.