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The Fork-Join task graph is one of the basic modeling structures for parallel processing. However, many previous scheduling algorithms ignore to economize processors and minimize the total completion time. What's more, many algorithms don't consider the competition caused by bus-based clusters and the heterogeneous of processors in real applications. This paper presents a new algorithm for Fork-Join task graph, considering economy of processors and minimization of the total completion time, the non-parallel communication, and heterogeneous environment as well. We propose a task scheduling algorithm based on task duplication which randomly generated a number of Fork-Join task graphs by producing the task execution time and communication time. Simulation results show that the proposed algorithm has less total completion time and less number of processors than other compared algorithms for more practical applications.

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The emerging multi-core processor architecture has greatly escalated scientific computing, but, at the same time, made parallel programming increasingly complex and challenging. In this paper, the use of the Auto Parallel Classification (APC) model in an Object-Oriented Parallel Model (OOPModel) environment is demonstrated. A designed module provides a traversal and a reduction of the DAG task graph. The parallel characteristics vectors, which are analyzed according to Naive Bayesian classification theory, are critical parameters for matching and generating parallel design patterns and various skeletal frameworks. Through extensive experimentation, it is demonstrated, that by using the Map-Reduce pattern to develop a minimumsort algorithm, in conjunction with the APC model, we can achieve a reduction in the complexity of parallel programming and the minimization of errors. Most importantly, through scientific experimentation, this document will further demonstrate that correct computational results and movements toward linear speedup can be accomplished.