L19-scheduling - Job Scheduling Lecture 19: March 19 Job...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 jobs-To minimize the completion time of all jobs (the makespan) NP-hard to approximate within 1.5 times of the optimal solution. Well design a 2-approximation 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 jobs-To 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....
View Full Document

Page1 / 29

L19-scheduling - Job Scheduling Lecture 19: March 19 Job...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online