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Delay-tolerant networks (DTNs) (e.g., Internet, satellite networks, sensor networks, ad hoc networks) have attracted considerable attentions in both academia and industry. As a fundamental problem, the maximum flow is of vital importance for routing and service scheduling in networks. For solving the maximum flow problem of the DTN, an appropriate model should be built first. Compared to the conventional snapshot approach to model the DTN topology, the time aggregated graph (TAG) is capable of accurately characterizing the intermittent connectivity and time-varying capacity for each edge, and thus has been acted as a suitable model for modeling DTNs. However, existing TAG-related works only focus on solving the shortest path problem, and neither the correlation between time intervals nor nodes storage of a DTN are described in TAG, resulting in a non-trivial maximum flow problem in TAG. In this paper …