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This paper studies the problem of scheduling a set of n independent tasks on m identical processors so as to minimize mean weighted flow-time. The problem is known to be NP-complete for m 2 and to be NP-complete in the strong sense for m arbitrary. The worst case behavior of a heuristic algorithm which requires time O (n n) is investigated, and it is shown that the mean weighted flow-time obtained by the algorithm does not exceed { (2 + 1) / 2} 1. 0207 times that of an optimal schedule. Moreover the bound { (2 + 1) / 2} is best possible.
Kawaguchi et al. (Sat,) studied this question.