Flow time scheduling with uncertain processing time

We consider the problem of online scheduling on a single machine in order to minimize weighted ow time. e existing algorithms for this problem (STOC '01, SODA '03, FOCS '18) all require exact knowledge of the processing time of each job. is assumption is crucial, as even a slight perturbation of the processing time would lead to polynomial competitive ratio. However, this assumption very rarely holds in real-life scenarios. In this paper, we present the rst algorithm for weighted ow time which do not require exact knowledge of the processing times of jobs. Speci cally, we introduce the Scheduling with Predicted Processing Time ( ) problem, where the algorithm is given a prediction for the processing time of each job, instead of its real processing time. For the case of a constant factor distortion between the predictions and the real processing time, our algorithms match all the best known competitiveness bounds for weighted ow time -namely O(log P ), O(log D) and O(log W ), where P, D, W are the maximum ratios of processing times, densities, and weights, respectively. For larger errors, the competitiveness of our algorithms degrades gracefully.