Various methods have been proposed in the literature to determine an optimal partitioning of the set of actors in a network into core and periphery subsets. However, these methods either work only for relatively small input sizes, or do not guarantee an optimal answer. In this paper, we propose a new algorithm to solve this problem. This algorithm is efficient and exact, allowing the optimal partitioning for networks of several thousand actors to be computed in under a second. We also show that the optimal core can be characterized as a set containing the actors with the highest degrees in the original network.