@MISC{Lecture_aptas, author = {In This Lecture}, title = {A PTAS for}, year = {} }

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Abstract

4> + \Delta: Since L is the average load of a machine, there must be another machine with a load less than the average. Assume without loss of generality, that this is machine 2, i.e., M 2 ! L. Therefore, we have M 1 \Gamma M 2 ! \Delta. Consider a schedule obtained by reassigning all the jobs, assigned to machine 1, except the job j, to machine 2. The contribution of machines 1 and 2 to the objective function in the new schedule is, then, (M 1 \Gamma \Delta) 2 + (M 2 + \Delta) 2 = M 2 1 +M 2 2 + 2\Delta(\Delta \Gamma (M 1 \Gamma M 2 )) M 2 1 +M 2 2 : Therefore, the new schedule has