Constructing an ∞‐steep Digraph by Flooding

This chapter presents an algorithm where the flooding starts from the black holes of the digraph and progresses following the ∞‐steep paths. It proposes the first version of the core‐expanding algorithm. It has the merit to show the structure of the algorithm, but it cannot be implemented as an executable algorithm, as it uses and computes infinite lexicographic weights. The chapter shows how the hierarchical queue (HQ) algorithm schedules the flooding. The choice of the flooding path to be kept is left to the HQ algorithm and the order in which the regional minima nodes have been introduced in the first‐in first‐out during the initialization phase. If only one flowing path remains for each node, this node is linked with one and only one regional minimum and belongs to only one catchment zone.