Flow Time Scheduling with Uncertain Processing Time

TL;DR

This paper introduces the first online scheduling algorithm for weighted flow time that operates effectively with predicted processing times instead of exact values, maintaining strong competitiveness under small prediction errors.

Contribution

It presents a novel algorithm for weighted flow time scheduling that handles uncertain processing times via predictions, achieving competitive bounds similar to traditional algorithms with perfect information.

Findings

Algorithms match best known bounds with accurate predictions

Competitiveness degrades gracefully with larger prediction errors

First to address scheduling with predicted processing times

Abstract

We consider the problem of online scheduling on a single machine in order to minimize weighted flow time. The existing algorithms for this problem (STOC '01, SODA '03, FOCS '18) all require exact knowledge of the processing time of each job. This 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 first algorithm for weighted flow time which do not require exact knowledge of the processing times of jobs. Specifically, we introduce the Scheduling with Predicted Processing Time (SPPT) 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 flow 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.