Improved upper bounds for online malleable job scheduling

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 $$m$$m identical machines. We study a model that accounts for the tradeoff between multiprocessor speedup and overhead time, namely, if job $$j$$j has processing requirement $$p_j$$pj and is assigned to run on $$k_j$$kj machines, then $$j$$j's execution time becomes $$p_j/k_j + (k_j -1)c$$pj/kj+(kj-1)c, where $$c$$c is a constant parameter to the problem. For $$m=2$$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 $$((4-\epsilon )/(3-\epsilon ))$$((4-∈)/(3-∈))-competitive when $$m=2$$m=2, where $$0 < \epsilon \le 2$$0<∈≤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 $$2$$2-competitive when $$m = 3$$m=3, improving upon the previous best upper bound of $$9/4$$9/4.