Efficient task scheduling is required to attain high performance in both homogeneous and heterogeneous computing systems. An application can be considered as a task grid represented using a Directed Acyclic Graph (DAG). Solving such DAG representing a scheduling problem is an NP-complete task. The primary concern in this problem domain is to reduce the schedule length with minimum complexity. This work presents a Hybrid List-based Task Scheduling using Duplication Scheme (HLTSD) algorithm for heterogeneous processors. The proposed HLTSD algorithm has the same time complexity as that of the recent state-of-the-art algorithms. However, it produces a minimum cost schedule in comparison with other related methods. This work also presents a mathematical formulation to find task priorities. The processor selection phase is improved by utilizing the techniques, like entry task duplication, insertion-based policy, duplication of parent task on other levels, and balancing the load on each processor. The current proposal minimizes the overall makespan of execution by reasonable levels. Performance of the proposed algorithm is evaluated using DAGs adopted from various state-of-the-art algorithms, real-world problems, like Gaussian elimination (GE) and fast Fourier transformation (FFT) task graph and randomly generated graphs with diverse characteristics. The proposed scheme is compared with four state-of-the-art list-based scheduling algorithms, namely Heterogeneous Earliest Finish Time (HEFT), Predict Earliest Finish Time (PEFT), Heterogeneous Scheduling with Improved task Priority (HSIP), and Task Scheduling for Heterogeneous Computing Systems (TSHCS). Based on the best quality schedule, the obtained results suggest that HLTSD has better results in 87% cases.

在同质和异质计算系统中都需要有效的任务调度来实现高性能。可以将应用程序视为使用有向无环图（DAG）表示的任务网格。解决这种表示调度问题的DAG是NP完成任务。此问题域中的主要关注点是以最小的复杂度来减少调度时间。这项工作提出了一种针对异构处理器的使用复制方案（HLTSD）算法的基于混合列表的任务调度。所提出的HLTSD算法具有与最新技术水平相同的时间复杂度。但是，与其他相关方法相比，它产生了最低的成本计划。这项工作还提出了数学公式来查找任务优先级。通过利用以下技术来改善处理器选择阶段，例如进入任务复制，基于插入的策略，父任务在其他级别上的复制以及平衡每个处理器上的负载。当前的建议将合理的执行范围最小化。使用从各种最新算法，实际问题（例如高斯消去（GE）和快速傅立叶变换（FFT）任务图）以及随机生成的具有多种特征的图样采用的DAG评估所提出算法的性能。将提出的方案与四种基于列表的最新调度算法进行了比较，即异构最早完成时间（HEFT），预测最早完成时间（PEFT），具有改进的任务优先级的异构调度（HSIP），和异构计算系统的任务计划（TSHCS）。根据最佳质量计划，所获得的结果表明，HLTSD在87％的病例中具有更好的结果。