How to minimize the number of mirroring resources under a QoS constraint (resource minimization problem) is an important issue in content delivery networks. This paper proposes a novel approach that takes advantage of the parallelism of dynamically reconfigurable processors (DRPs) to solve the resource minimization problem, which is NP-hard. Our proposal obtains the optimal solution by running an exhaustive search algorithm suitable for DRP. Greedy algorithms, which have been widely studied for tackling the resource minimization problem, cannot always obtain the optimal solution. The proposed method is implemented on an actual DRP and in experiments reduces the execution time by a factor of 40 compared to the conventional exhaustive search algorithm on a Pentium 4 (2.8GHz).