Non-Preemptive Flow-Time Minimization via Rejections

Authors Anupam Gupta, Amit Kumar, Jason Li

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Author Details

Anupam Gupta
  • Carnegie Mellon University
Amit Kumar
  • IIT Delhi
Jason Li
  • Carnegie Mellon University

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Anupam Gupta, Amit Kumar, and Jason Li. Non-Preemptive Flow-Time Minimization via Rejections. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 70:1-70:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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 epsilon-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 argument to bound the flow-time. Indeed, we use the dual-fitting framework, with considerable more machinery to certify that the cost of our algorithm is within a constant of the optimum while only a small fraction of the jobs are rejected.

Subject Classification

ACM Subject Classification
  • Theory of computation → Scheduling algorithms
  • Scheduling
  • Rejection
  • Unrelated Machines
  • Non-Preemptive


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