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Reallocation Problems in Scheduling

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Abstract

In traditional on-line problems, such as scheduling, requests arrive over time, demanding available resources. As each request arrives, some resources may have to be irrevocably committed to servicing that request. In many situations, however, it may be possible or even necessary to reallocate previously allocated resources in order to satisfy a new request. This reallocation has a cost. This paper shows how to service the requests while minimizing the reallocation cost. We focus on the classic problem of scheduling jobs on a multiprocessor system. Each unit-size job has a time window in which it can be executed. Jobs are dynamically added and removed from the system. We provide an algorithm that maintains a valid schedule, as long as a schedule with sufficient slack exists. The algorithm reschedules only a total number of \(O(\min \{\log ^*{n}, \log ^*{\varDelta }\})\) jobs for each job that is inserted or deleted from the system, where \(n\) is the number of active jobs and \(\varDelta \) is the size of the largest window.

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Notes

  1. Before you get too skeptical about the motivation, this is exactly what M. F-C’s ophthalmologist does.

  2. At first glance, Lemma 3 seems to contradict the underallocation requirement given in Lemma 8. That lower bound, however, applies to the general case, whereas this lemma applies to the aligned case.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Stony Brook University, Stony Brook, NY, 11794-4400, USA

    Michael A. Bender

  2. Tokutek, Inc., New York, NY, USA

    Michael A. Bender & Martin Farach-Colton

  3. Department of Computer Science, Rutgers University, Piscataway, NJ, 008855, USA

    Martin Farach-Colton

  4. Department of Computer Science, TU Braunschweig, 38106, Braunswick, Germany

    Sándor P. Fekete

  5. Department of Computer Science, Georgetown University, Washington, DC, 20057, USA

    Jeremy T. Fineman

  6. Department of Computer Science, National University of Singapore, Singapore, 119077, Singapore

    Seth Gilbert

Authors
  1. Michael A. Bender
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  2. Martin Farach-Colton
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  3. Sándor P. Fekete
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  4. Jeremy T. Fineman
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  5. Seth Gilbert
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Corresponding author

Correspondence to Sándor P. Fekete.

Additional information

This research was supported in part by NSF grants IIS 1247726, IIS 1251137, IIS 1247750, CCF 1114930, CCF 1217708, CCF 1114809, CCF 0937822, CCF 1218188, by DFG grant FE407/17-1, and by Singapore NUS FRC R-252-000-443-133. A preliminary version appears in SPAA 2013 [8].

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Bender, M.A., Farach-Colton, M., Fekete, S.P. et al. Reallocation Problems in Scheduling. Algorithmica 73, 389–409 (2015). https://doi.org/10.1007/s00453-014-9930-4

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