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In wireless mobile environments, data broadcasting is an effective approach to disseminate information to mobile clients. In some applications, the access pattern of all the data to be downloaded can be represented by a DAG. In this paper, we consider the problem of efficiently generating the broadcast schedule on multiple channels when the data set has a DAG access pattern. We prove that it is NP-hard to find an optimal broadcast schedule which not only minimizes the latency but also satisfies the ancestor property which preserves the data dependency. We further rule out a condition for the input DAGs under which one can generate an optimal broadcast schedule in linear time and propose an algorithm, LBS, to generate the schedule under such a condition. For general DAGs, we provide three heuristics: the first one uses the overall access probability of each vertex; the second one considers the total access probability of a vertex's descendants; the third one combines the above two heuristics. We analyze these three heuristics and compare them through experiments. Our result shows that the third one can achieve a better broadcast schedule in terms of overall latency but costs more running time.