The Efficiency of MapReduce in Parallel External Memory

Since its introduction in 2004, the MapReduce framework has be-come one of the standard approaches in massive distributed and paral-lel computation. In contrast to its intensive use in practise, theoretical footing is still limited and only little work has been done yet to put MapReduce on a par with the major computational models. Follow-ing pioneer work that relates the MapReduce framework with PRAM and BSP in their macroscopic structure, we focus on the functionality provided by the framework itself, considered in the parallel external memory model (PEM). In this, we present upper and lower bounds on the parallel I/O-complexity that are matching up to constant factors for the shuffle step. The shuffle step is the single communication phase where all information of one MapReduce invocation gets transferred from map workers to reduce workers. Hence, we move the focus to-wards the internal communication step in contrast to previous work. The results we obtain further carry over to the BSP ∗ model. On the one hand, this shows how much complexity can be “hidden ” for an algo-rithm expressed in MapReduce compared to PEM. On the other hand, our results bound the worst-case performance loss of the MapReduce approach in terms of I/O-efficiency.