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Online Non-preemptive Scheduling to Optimize Max Stretch on a Single Machine

  • Pierre-Francois Dutot
  • Erik Saule
  • Abhinav SrivastavEmail author
  • Denis Trystram
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9797)

Abstract

We consider in this work a classical online scheduling problem with release times on a single machine. The quality of service of a job is measured by its stretch, which is defined as the ratio of its response time over its processing time. Our objective is to schedule the jobs non-preemptively in order to optimize the maximum stretch. We present both positive and negative theoretical results. First, we provide an online algorithm based on a waiting strategy which is \((1+\frac{\sqrt{5}-1}{2}\varDelta )\)-competitive where \(\varDelta \) is the upper bound on the ratio of processing times of any two jobs. Then, we show that no online algorithm has a competitive ratio better than \(\frac{\sqrt{5}-1}{2}\varDelta \). The proposed algorithm is asymptotically the best algorithm for optimizing the maximum stretch on a single machine.

Notes

Acknowledgments

This work has been partially supported by the LabEx PERSYVAL-Lab (ANR-11-LABX-0025-01) funded by the French program Investissement d’avenir. Erik Saule is a 2015 Data Fellow of the National Consortium for Data Science (NCDS) and acknowledges the NCDS for funding parts of the presented research.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Pierre-Francois Dutot
    • 1
  • Erik Saule
    • 2
  • Abhinav Srivastav
    • 1
    Email author
  • Denis Trystram
    • 1
  1. 1.University of Grenoble AlpesSaint-Martin-d’HèresFrance
  2. 2.Department of Computer ScienceUniversity of North Carolina at CharlotteCharlotteUSA

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