Despite crucial recent advances, the problem of frequent itemset mining is still facing major challenges. This is particularly the case when: i) the mining process must be massively distributed and; ii) the minimum support (MinSup) is very low. In this paper, we study the effectiveness and leverage of specific data placement strategies for improving parallel frequent itemset mining (PFIM) performance in MapReduce, a highly distributed computation framework. By offering a clever data placement and an optimal organization of the extraction algorithms , we show that the itemset discovery effectiveness does not only depend on the deployed algorithms. We propose ODPR (Optimal Data-Process Relationship), a solution for fast mining of frequent itemsets in MapReduce. Our method allows discovering itemsets from massive datasets, where standard solutions from the literature do not scale. Indeed, in a massively distributed environment, the arrangement of both the data and the different processes can make the global job either completely inoperative or very effective. Our proposal has been evaluated using real-world data sets and the results illustrate a significant scale-up obtained with very low MinSup, which confirms the effectiveness of our approach.