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MapReduce is a popular paradigm in distributed computing, but it is not efficient when executing iterative algorithms over a distributed big dataset due to its heavy data communication overhead. Non-MapReduce computing is an alternative for improving computing efficiency and data scalability when using iterative algorithms to process big distributed datasets on clusters. In this paper, we investigate Non-MapReduce approach in distributed computing and use Spark implementations of machine learning algorithms to discuss the problems of MapReduce in executing iterative algorithms over a big distributed dataset and the advantages of Non-MapReduce for the same tasks. We present a method to build a new machine learning library made of sequential algorithms for distributed computing. We use experiment results to show comparisons of computing efficiency and data scalability of MapReduce and Non-MapReduce in executing six machine learning algorithms over big datasets. [ABSTRACT FROM AUTHOR]