  MapReduce is a popular parallel computing paradigm for Big Data processing in
clusters and data centers. It is observed that different job execution orders
and MapReduce slot configurations for a MapReduce workload have significantly
different performance with regarding to the makespan, total completion time,
system utilization and other performance metrics. There are quite a few
algorithms on minimizing makespan of multiple MapReduce jobs. However, these
algorithms are heuristic or suboptimal. The best known algorithm for minimizing
the makespan is 3-approximation by applying Johnson rule. In this paper, we
propose an approach called UAAS algorithm to meet the conditions of classical
Johnson model. Then we can still use Johnson model for an optimal solution. We
explain how to adapt to Johnson model and provide a few key features of our
proposed method.
