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In this paper, we introduce a new online scheduling framework for minimizing total weighted completion time in a general setting. The framework is inspired by the work of Hall et al. [10] and Garg et al. [8], who show how to convert an offline approximation to an online scheme. Our framework uses two offline approximation algorithms—one for the simpler problem of scheduling without release times, and another for the minimum unscheduled weight problem—to create an online algorithm with provably good competitive ratios.

Select and Permute: An Improved Online Framework for Scheduling to Minimize Weighted Completion Time