On Approximation Algorithms for Two-Stage Scheduling Problems
We study scheduling on parallel two-stage flowshops in which each job has to pass through two operations: an R-operation and a T-operation. Motivated by the current research in data centers, we consider two restricted versions of the problem: one restricts that for each job, the R-operation consumes no less time than the T-operation, while the other assumes that the T-operation takes more time than the R-operation for each job. For the first case, we present an online 2-competitive algorithm and an offline 11/6-approximation algorithm. For the second case, we give an online 5/2-competitive algorithm, and prove, for the offline setting, that the problem can be reduced to the problem in the first case.
KeywordsCompletion Time Approximation Ratio Competitive Ratio Online Algorithm Online Schedule
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