We study the problem of minimizing total completion time on parallel machines subject to varying processing capacity. In this paper, we develop an approximation scheme for the problem under the data stream model where the input data is massive and cannot fit into memory and thus can only be scanned for a few passes. Our algorithm can compute the approximate value of the optimal total completion time in one pass and output the schedule with the approximate value in two passes.
Fu, Bin, Yumei Huo, and Hairong Zhao. "Streaming Approximation Scheme for Minimizing Total Completion Time on Parallel Machines Subject to Varying Processing Capacity." arXiv preprint arXiv:2204.01976 (2022).