Heterogeneous system list scheduling algorithm based on improved optimistic cost matrix

In heterogeneous computing systems, efficient task-scheduling methods are paramount for enhancing computational performance. However, the existing algorithm exhibits certain deficiencies, notably its oversight of load balancing concerns and inadequate emphasis on the out-degree property of tasks. To address these issues, a novel list scheduling algorithm is proposed, Average Earliest Finish Time (AEFT), which proficiently allocates task flows onto heterogeneous processors. The AEFT algorithm primarily consists of two key stages: (1) prioritizing tasks to determine the distribution of task priorities and (2) assigning optimal processors for tasks with given priorities. By leveraging its specific topology, the AEFT algorithm minimizes the scheduling length of task flows. Simultaneously, a prediction mechanism in determining task prioritization and selecting processors stages is proposed to reduce the scheduling time of task flows. In addition, in the processor selection stage, AEFT algorithm considers the out-degree characteristics of tasks, ameliorating situations of processor load imbalance. The AEFT algorithm demonstrates superior performance compared to prior list scheduling algorithms concerning makespan, speedup, and the percentage of occurrences of better solutions, as evidenced by experiments conducted on randomly generated and real-application graphs. Specifically, for $t$ tasks and $p$ processors, the AEFT algorithm achieves a time complexity of $O\left(t^{2}p\right)$.