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It might be argued that we could wait till the Task C to finish during this checkpoint, then we could not trigger task C in the checkpoints. However, this does not work if C is a two-phase commit sink and requires one successful checkpoint before finish, which will cause deadlock.

To find the new "root" of the current execution graph, we iterates from the 

The basic algorithm to compute the tasks to trigger would be iterating over the ExecutionGraph to find the new root running tasks. However, the algorithm could be optimized by iterating over the JobGraph instead. The detailed algorithm is shown in Appendix. 

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