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Determining loss minimum configuration in a distribution network is a hard discrete optimization problem involving many variables. Since more and more dispersed generators are installed on the demand side of power systems and they are reconfigured frequently, developing automatic approaches is indispensable for effectively managing a large-scale distribution network. Existing fast methods employ local updates that gradually improve the loss to solve such an optimization problem. However, they eventually get stuck at local minima, resulting in arbitrarily poor results. In contrast, this paper presents a novel optimization method that provides an error bound on the solution quality. Thus, the obtained solution quality can be evaluated in comparison to the global optimal solution. Instead of using local updates, we construct a highly compressed search space using a binary decision diagram and reduce the optimization problem to a shortest path-finding problem. Our method was shown to be not only accurate but also remarkably efficient; optimization of a large-scale model network with 468 switches was solved in three hours with 1.56% relative error bound.