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Unformatted text preview: Job Scheduling Lecture 19: March 19 Job Scheduling: Unr elated Multiple Machines There are n jobs , each job has: a processing time p(i,j) (the time to finish this job j on machine i ) There are m machine available. Task : to scheduling the jobsTo minimize the completion time of all jobs (the makespan) NPhard to approximate within 1.5 times of the optimal solution. Well design a 2approximation algorithm for this problem. Why Unr elated? For example, different processors have different specialties. Computational jobs, display images, etc Job Scheduling: Unr elated Multiple Machines There are n jobs , each job has: a processing time p(i,j) (the time to finish this job j on machine i ) There are m machine available. Task : to scheduling the jobsTo minimize the completion time of all jobs (the makespan) Approach: Linear Pr ogr amming . How to formulate this problem into linear program? Linear Pr ogr amming Relaxation whether job j is scheduled in machine i for each job j Each job is scheduled in one machine. for each machine i Each machine can finish its jobs by time T for each job j, machine i Relaxation H ow good is this r elaxation? for each job j for each machine i for each job j, machine i Example One job of processing time K for each machine Optimal solution = K. Optimal fraction solution = K/ m. The LP lower bound could be very bad. H ow good is the r elaxation? for each job j for each machine i for each job j, machine i Example One job of processing time K for each machine Optimal solution = K. Optimal fraction solution = K/ m. Pr oblem of the linear pr ogr am r elaxation : an optimal solution T could be even smaller than the processing time of a job! H ow to tackle this pr oblem? Pr oblem of the linear pr ogr am r elaxation : an optimal solution T could be even smaller than the processing time of a job! I deally, we could write the following constraint: but this is not a linear constraint I dea? To enforce this constraint by pr epr ocessing ! Pr epr ocessing Fix T....
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 Spring '09
 xulei

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