We present a new algorithm for solving the common problem of flow trapped in closed depressions within digital elevation models, as encountered in many applications relying on flow routing. Unlike other approaches (e.g., the so-called "Priority-Flood" depression filling algorithm), this solution is based on the explicit computation of the flow paths both within and across the depressions through the construction of a graph connecting together all adjacent drainage basins. Although this represents 5 many operations, a linear time-complexity can be reached for the whole computation, making it very efficient. Compared to the most optimized solutions proposed so far, we show that this algorithm of flow path enforcement yields the best performance when used in landscape evolution models. Besides its efficiency, our proposed method has also the advantage of letting the user choose among different strategies of flow path enforcement within the depressions (i.e., filling vs. carving). Furthermore, the computed graph of basins is a generic structure that has the potential to be reused for solving other problems as well , such as the simulation of erosion. This sequential algorithm may be helpful for those who need to, e.g., process digital elevation models of moderate size on single computers or run batches of simulations as part of an inference study.