Non-Preemptive Flow-Time Minimization via Rejections

TL;DR

This paper introduces the first constant-competitive algorithm for non-preemptive weighted flow-time minimization on unrelated machines, allowing limited job rejection to achieve near-optimal scheduling performance.

Contribution

It presents a novel algorithm that handles non-preemptive scheduling with job rejection, extending the understanding of flow-time minimization in the weakest known rejection model.

Findings

Achieves constant competitiveness in non-preemptive setting

Uses a delicate dual-fitting analysis for flow-time bounds

Allows rejection of a small fraction of total job weight

Abstract

We consider the online problem of minimizing weighted flow-time on unrelated machines. Although much is known about this problem in the resource-augmentation setting, these results assume that jobs can be preempted. We give the first constant-competitive algorithm for the non-preemptive setting in the rejection model. In this rejection model, we are allowed to reject an $\varepsilon$-fraction of the total weight of jobs, and compare the resulting flow-time to that of the offline optimum which is required to schedule all jobs. This is arguably the weakest assumption in which such a result is known for weighted flow-time on unrelated machines. While our algorithms are simple, we need a delicate dual-fitting argument to bound the flow-time while only a small fraction of elements are rejected.