In this paper, we study online algorithms that schedule malleable jobs, i.e., jobs that can be par allelized 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 pj and is assigned to run on kj machines, then J ’s execution time becomes Pj/kj + (kj — l)c, where c is a constant parameter to the problem. When 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 — e)∕(3 — e))- competitive when m = 2, where 0 < e ≤ 2 is a parameter to the algorithm.
Kell, Nathaniel, "Improved Upper Bounds for Online Malleable Job Scheduling" (2013). Student Scholarship. 146.