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We consider the problem of scheduling jobs to minimize the maximum weighted flow-time on a set of related machines. When jobs can be preempted this problem is well-understood; for example, there exists a constant competitive algorithm using speed augmentation. When jobs must be scheduled non-preemptively, only hardness results are known. In this paper, we present the first online guarantees for the non-preemptive variant. We present the first constant competitive algorithm for minimizing thedoi:10.4230/lipics.fsttcs.2019.24 dblp:conf/fsttcs/LucarelliMTST19 fatcat:3gknfaamyzb6ref7ja2kkeajjq