License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.ESA.2018.59
URN: urn:nbn:de:0030-drops-95226
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Lucarelli, Giorgio ; Moseley, Benjamin ; Thang, Nguyen Kim ; Srivastav, Abhinav ; Trystram, Denis

Online Non-Preemptive Scheduling to Minimize Weighted Flow-time on Unrelated Machines

LIPIcs-ESA-2018-59.pdf (0.4 MB)


In this paper, we consider the online problem of scheduling independent jobs non-preemptively so as to minimize the weighted flow-time on a set of unrelated machines. There has been a considerable amount of work on this problem in the preemptive setting where several competitive algorithms are known in the classical competitive model. However, the problem in the non-preemptive setting admits a strong lower bound. Recently, Lucarelli et al. presented an algorithm that achieves a O(1/epsilon^2)-competitive ratio when the algorithm is allowed to reject epsilon-fraction of total weight of jobs and has an epsilon-speed augmentation. They further showed that speed augmentation alone is insufficient to derive any competitive algorithm. An intriguing open question is whether there exists a scalable competitive algorithm that rejects a small fraction of total weights.
In this paper, we affirmatively answer this question. Specifically, we show that there exists a O(1/epsilon^3)-competitive algorithm for minimizing weighted flow-time on a set of unrelated machine that rejects at most O(epsilon)-fraction of total weight of jobs. The design and analysis of the algorithm is based on the primal-dual technique. Our result asserts that alternative models beyond speed augmentation should be explored when designing online schedulers in the non-preemptive setting in an effort to find provably good algorithms.

BibTeX - Entry

  author =	{Giorgio Lucarelli and Benjamin Moseley and Nguyen Kim Thang and Abhinav Srivastav and Denis Trystram},
  title =	{{Online Non-Preemptive Scheduling to Minimize Weighted Flow-time on Unrelated Machines}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{59:1--59:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Yossi Azar and Hannah Bast and Grzegorz Herman},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-95226},
  doi =		{10.4230/LIPIcs.ESA.2018.59},
  annote =	{Keywords: Online Algorithms, Scheduling, Resource Augmentation}

Keywords: Online Algorithms, Scheduling, Resource Augmentation
Collection: 26th Annual European Symposium on Algorithms (ESA 2018)
Issue Date: 2018
Date of publication: 14.08.2018

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