Brief Announcement: Towards a More Robust Algorithm for Flow Time Scheduling with Predictions

We consider the problem of non-clairvoyant scheduling on single machine to minimize the total flow time with job size predictions. The existing algorithm achieves 2-consistency to predictions, but no algorithm can simultaneously attain bounded robustness. This work finds a sufficient condition for any algorithm to achieve optimal O(P)-robustness, where P is the maximum ratio of any two job sizes. We give the first algorithm that achieves optimal robustness up to a constant multiplicative factor and optimal consistency using this condition. Finally, for addressing small prediction errors, we present an algorithm that we conjecture to achieve the optimal O(η^2) competitive ratio, where η is the prediction error. Proving the claimed bound is our ongoing work.