Xxa Ptas for Minimizing Thetotal Weighted Completion Timeon Identical Parallel

We consider the problem of scheduling a set of n jobs on m identical parallel machines so as to minimize the weighted sum of job completion times. This problem is NP-hard in the strong sense. The best approximation result known so far was a 1 2 (1 + p 2){approximation algorithm that has been derived by Kawaguchi and Kyan back in 1986. The contribution of this paper is a polynomial time approximation scheme for this setting, which settles a problem that was open for a long time. Moreover, our result constitutes the rst known approximation scheme for a strongly NP-hard scheduling problem with minsum objective.