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In this paper, we give a characterization of the rate region for the degraded two message set problem, applied to a combination network with erasure channels. We also provide an algorithm that uses topological information in order to deliver the two messages to the receivers, and we show that our algorithm is optimal, in the sense that it achieves any rate pair in the region. We compare our algorithm analytically with a naive approach oblivious to the network structure, and we give an insight on what benefits should be expected for different classes of networks.