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On the Value of Job Migration in Online Makespan Minimization

  • Susanne Albers
  • Matthias Hellwig
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7501)

Abstract

Makespan minimization on identical parallel machines is a classical scheduling problem. We consider the online scenario where a sequence of n jobs has to be scheduled non-preemptively on m machines so as to minimize the maximum completion time of any job. The best competitive ratio that can be achieved by deterministic online algorithms is in the range [1.88,1.9201]. Currently no randomized online algorithm with a smaller competitiveness is known, for general m.

In this paper we explore the power of job migration, i.e. an online scheduler is allowed to perform a limited number of job reassignments. Migration is a common technique used in theory and practice to balance load in parallel processing environments. As our main result we settle the performance that can be achieved by deterministic online algorithms. We develop an algorithm that is α m -competitive, for any m ≥ 2, where α m is the solution of a certain equation. For m = 2, α 2 = 4/3 and lim m → ∞  α m  = W − 1( − 1/e 2)/(1 + W − 1( − 1/e 2)) ≈ 1.4659. Here W − 1 is the lower branch of the Lambert W function. For m ≥ 11, the algorithm uses at most 7m migration operations. For smaller m, 8m to 10m operations may be performed. We complement this result by a matching lower bound: No online algorithm that uses o(n) job migrations can achieve a competitive ratio smaller than α m . We finally trade performance for migrations. We give a family of algorithms that is c-competitive, for any 5/3 ≤ c ≤ 2. For c = 5/3, the strategy uses at most 4m job migrations. For c = 1.75, at most 2.5m migrations are used.

Keywords

Competitive Ratio Online Algorithm Online Schedule Makespan Minimization Loaded Machine 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Susanne Albers
    • 1
  • Matthias Hellwig
    • 1
  1. 1.Department of Computer ScienceHumboldt-Universität zu BerlinGermany

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