Recommending a sequence of items that maximizes some objective function arises in many real-world applications. In this paper, we consider a utility function over sequences of items where sequential dependencies between items are modeled using a directed graph. We propose EdGe, an efficient greedy algorithm for this problem and we demonstrate its effectiveness on both synthetic and real datasets. We show that EdGe achieves comparable recommendation precision to the state-of-the-art related work OMEGA, and in considerably less time. This work opens several new directions that we discuss at the end of the paper.