The effective construction of many association rule bases require the computation of frequent closures, generators, and precedence links between closures. However, these tasks are rarely combined, and no scalable algorithm exists at present for their joint computation. We propose here a method that solves this challenging problem in two separated steps. First, we introduce a new algorithm called Touch for finding frequent closed itemsets (FCIs) and their generators (FGs). Touch applies depth-first traversal, and experimental results indicate that this algorithm is highly efficient and outperforms its levelwise competitors. Second, we propose another algorithm called Snow for extracting efficiently the precedence from the output of Touch. To do so, we apply hypergraph theory. Snow is a generic algorithm that can be used with any FCI/FG-miner. The two algorithms, Touch and Snow, provide a complete solution for constructing iceberg lattices. Furthermore, due to their modular design, parts of the algorithms can also be used independently.