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We consider the problem of accessing large data files stored at multiple locations across a content distribution, peer-to-peer, or massive storage network. We assume that the data is stored in either original form, or encoded form at multiple network locations. Clients access the data through simultaneous downloads from several servers across the network. The central problem in this context is to find a set of disjoint paths of minimum total cost that connect the client with a set of servers such that the data stored at the servers is sufficient to decode the required file. We refer to this problem as the Distributed Data Retrieval (DDR) problem. We present an efficient polynomial-time solution for this problem that leverages the matroid intersection algorithm. Our experimental study shows the advantage of our solution over alternative approaches.