CS 294 - 128 : Algorithms and Uncertainty Lecture 5 Date
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چکیده
We begin by recalling the flow time minimization problem on unrelated machines from last lecture: Given a set of machines and a set of jobs, define: rj ∈ Z, to be the release time of job j, pi,j ∈ Z, is the run time of job j on machine i, Cj is the time at which job j is completed and the flow time of j is Fj = Cj − rj . Our goal is to find a schedule S, s.t. ∑ j∈J Fj is minimized. In the online setting, jobs arrive over time and no assumptions can be made about pi,j or rj before job j arrives. In addition, we make two additional requirements from the algorithm. Once a job is assigned to a machine, it cannot be migrated to another machine. Jobs may be paused and continued at a later date in the future. This is called preemption. In fact our algorithm will assign a job to machine immediately upon arrival. Such algorithms are called immediate dispatch algorithms. We first observe that the algorithm only needs to specify which machine to assign a job. This is because given an assignment of jobs to a machine, we simply run the SRPT (Shortest Remaining Processing Time) algorithm on that machine, which is optimum (1-competitive). Consider the following algorithm for a single machine system (Shortest Remaining Processing Time) which at any time works on the job with the least remaining processing (note that it only preempts a job upon the arrival on another job).
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تاریخ انتشار 2016