Consider the following preemptive variant of the Load Balancing problem: There are m identical machines, and...

  

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Consider the following preemptive variant of the Load Balancing problem: There are m identical machines, and n jobs with processing times t₁, t2,, tn respectively. Each machine can process at most one job at a time. Each job can run on more than one machines but must run on at most one machine at any time. Let T = max {maxisj≤ntj, E₁<i<nt;}. (a) Prove that the optimal makespan is at least T. (b) Give a linear-time algorithm which produces a preemptive schedule with makespan exactly T. Consider the following preemptive variant of the Load Balancing problem: There are m identical machines, and n jobs with processing times t₁, t2,, tn respectively. Each machine can process at most one job at a time. Each job can run on more than one machines but must run on at most one machine at any time. Let T = max {maxisj≤ntj, E₁<i<nt;}. (a) Prove that the optimal makespan is at least T. (b) Give a linear-time algorithm which produces a preemptive schedule with makespan exactly T.

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