A Note on “Orchestrating an Ensemble of MapReduce Jobs for Minimizing Their Makespan”

In paper [1], a scheduling model is considered for multiple MapReduce jobs. The goal in [1] is to design an automatic job scheduler that minimizes the makespan of such a set of MapReduce jobs. In this work, we find that there is a key assumption in [1] which leads to the violation of the conditions for classical Johnson's algorithm and a suboptimal job scheduling for minimizing total makespan. By considering a better strategy and implementation, we can still meet the conditions of classical Johnson's algorithm. Then we can still use Johnson's algorithm for an optimal solution. As for BalancedPools algorithm proposed in paper [1], under our proposed new strategy, it is possible to solve it exactly in linear time, but not NP-hard as suggested in [1], the proof is provided. With the new strategy, results obtained in [1] need reevaluating.