Journal of Scheduling

, Volume 18, Issue 4, pp 393–410 | Cite as

Improved upper bounds for online malleable job scheduling



In this paper, we study online algorithms that schedule malleable jobs, i.e., jobs that can be parallelized on any subset of the available \(m\) identical machines. We study a model that accounts for the tradeoff between multiprocessor speedup and overhead time, namely, if job \(j\) has processing requirement \(p_j\) and is assigned to run on \(k_j\) machines, then \(j\)’s execution time becomes \(p_j/k_j + (k_j -1)c\), where \(c\) is a constant parameter to the problem. For \(m=2\), we present an online algorithm OCS that has a strong competitive ratio of 3/2, matching a previously established lower bound. We also present an online algorithm ASYM2 that is asymptotically \(((4-\epsilon )/(3-\epsilon ))\)-competitive when \(m=2\), where \(0 < \epsilon \le 2\) is a parameter to the algorithm, improving upon an existing asymptotically (3/2)-competitive algorithm. Finally, we present an online algorithm OTO that is strongly \(2\)-competitive when \(m = 3\), improving upon the previous best upper bound of \(9/4\).


Online algorithms Scheduling Parallel jobs Identical machines Overhead time 


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Computer ScienceDuke UniversityDurhamUSA
  2. 2.Department of Mathematics and Computer ScienceDenison UniversityGranvilleUSA

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