# Improved upper bounds for online malleable job scheduling

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## Abstract

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 \(9/4\).

## Keywords

Online algorithms Scheduling Parallel jobs Identical machines Overhead time## References

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