Formal Derivation of Distributed MapReduce

MapReduce is a powerful distributed data processing model that is currently adopted in a wide range of domains to efficiently handle large volumes of data, i.e., cope with the big data surge. In this paper, we propose an approach to formal derivation of the MapReduce framework. Our approach relies on stepwise refinement in Event-B and, in particular, the event refinement structure approach -- a diagrammatic notation facilitating formal development. Our approach allows us to derive the system architecture in a systematic and well-structured way. The main principle of MapReduce is to parallelise processing of data by first mapping them to multiple processing nodes and then merging the results. To facilitate this, we formally define interdependencies between the map and reduce stages of MapReduce. This formalisation allows us to propose an alternative architectural solution that weakens blocking between the stages and, as a result, achieves a higher degree of parallelisation of MapReduce computations.