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We consider the online problem of scheduling jobs on unrelated machines so as to minimize the total weighted flow time. This problem has an unbounded competitive ratio even for very restricted settings. In this paper we show that if we allow the machines of the online algorithm to have more speed than those of the offline algorithm then we can get an O((1 + −1 ) 2 )-competitive algorithm. Our algorithm schedules jobs preemptively but without migration. However, we compare our solution to andoi:10.1145/1536414.1536506 dblp:conf/stoc/ChadhaGKM09 fatcat:hbylkj6ye5hp7daipvk4ynhyea