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In this paper, we consider a multi-user optical grid environment where the optical grid network is shared among multiple users who have a high demand for data processing. In such multi-user grid environment, since the supercomputer can start the data processing only after the corresponding data file has reached it, one critical problem is how to effectively schedule large data file transfers on the optical grid network. In this paper, we propose four dynamic scheduling algorithms to address the issue of large file transfers on multi-user optical grid network. Two objectives, namely the efficiency and fairness, are considered to evaluate the performance of each scheduling algorithm. Efficiency aims at how to achieve the best overall quality of grid service, and fairness regards the service quality deviation among grid users. We study the performance of each algorithm, and a tradeoff between efficiency and fairness is shown by our results.