Before revision:  The modified SRPT algorithm is shown to achieve a competitive ratio of \Theta(\log \alpha +\beta) for minimizing the flow time, where \alpha denotes the ratio of maximum job workload and minimum job workload, \beta represents the ratio between maximum non-preemptive task workload and minimum job workload.
After revision:  The M-SRPT algorithm is proved to achieve a competitive ratio of \Theta(\log \alpha +\beta) for minimizing the flow time, where \alpha denotes the ratio of maximum job workload and minimum job workload, \beta represents the ratio between maximum non-preemptive task workload and minimum job workload.