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Fault-tolerant scheduling is an imperative step for large-scale computational grid systems, as often geographically distributed nodes co-operate to execute a task. By and large, primary-backup approach is a common methodology used for fault tolerance wherein each task has a primary copy and a backup copy on two different processors. In this paper, we identify two cases that may happen when scheduling dependent tasks with primary-backup approach. We derive two important constraints that must be satisfied. Further, we show that these two constraints play a crucial role in limiting the schedulability and overloading efficiency of backups of dependent tasks. We then propose two strategies to improve schedulability and overloading efficiency, respectively. We propose two algorithms (MRC-ECT and MCT-LRC), to schedule backups of independent jobs and dependent jobs, respectively. MRC-ECT is shown to …