Scheduling Problem Notes

Scheduling Problem Notes - 1 Notes on the Online Load...

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1 Notes on the Online Load Balancing/Scheduling Algorithms Definitions and Observations If j is a job, its load is denoted r j . An input sequence of jobs is denoted by their loads σ = r 1 , r 2 , . . . r N The optimal algorithm that minimizes the max load in the system is denoted by OPT ( σ ) . Jobs are permanent (think daemons), i.e once assigned they keep executing. You can imagine multiple jobs assigned to a machine share the load. For related machines, the load (cost) of a job j on machine i is r j ( i ) = v j α i . So all machines can be ranked in increasing order of cost r j ( i ) from the perspective of job j . Assume this results in the ordering M 1 , M 2 , . . . M M , i.e r j (1) > r j (2) > . . . . For identical machines, i, α i = 1 . Greedy Algorithm on Identical Machines : Assign a job to the machine with lowest current load. If there are ties, break them arbitrarily. You can show that this is 2 - 1 M -competitive. Assume A is a known upper bound on the cost of OPT ( σ ) .

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