Scheduling with a processing time oracle
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In this paper we study a single machine scheduling problem on a set of independent jobs whose execution time is not known, but guaranteed to be either short or long, for two given processing times. At every time step, the scheduler has the possibility either to test a job, by querying a processing time oracle, which reveals its processing time, and occupies one time unit on the schedule. Or the scheduler can execute a job, might it be previously tested or not. The objective value is the total completion time over all jobs, and is compared with the objective value of an optimal schedule, which does not need to test. The resulting competitive ratio measures the price of hidden processing time. Two models are studied in this paper. In the non-adaptive model, the algorithm needs to decide before hand which jobs to test, and which jobs to execute untested. However in the adaptive model, the algorithm can make these decisions adaptively to the outcomes of the job tests. In both models we provide optimal polynomial time two-phase algorithms, which consist of a first phase where jobs are tested, and a second phase where jobs are executed untested. Experiments give strong evidence that optimal algorithms have this structure. Proving this property is left as an open problem.
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