The paper introduces a new concept of submodularity, which is called the adaptive sequence submodularity defined on directed graphs and hypergraphs. The model is interesting and has a wealth of important applications. The propose an algorithm with strong theoretical guarantees. The analysis in the adaptive setting is not trivial and there are new and interesting ideas introduced. Furthermore, the authors show that this algorithm has strong guarantees for special cases of the problem studied in the past. In addition, the authors perform a series of experiments on interesting applications, showing their effectiveness in practice. This is a well written paper, which introduces a new model that captures important applications, new algorithmic techniques, improves on special cases from previous work, and performs rigorous experiments. We therefore strongly recommend on accepting this paper.