Scheduling with a processing time oracle

In this paper we study a single machine scheduling problem with the objective of minimizing sum completion times. Each given jobs is either short or long. However processing times are initially hidden to algorithm, but can be tested. This done by executing time oracle, which reveals job. test occupies unit in schedule, therefore algorithm must decide for it will call oracle. The value resulting schedule compared an optimal computed using full information. competitive ratio measures price times, and goal design minimal ratio. Two models studied paper. non-adaptive model, needs beforehand test, execute untested. adaptive make these decisions adaptively depending on outcomes job tests. both provide polynomial algorithms following two-phase strategy, consist first phase where tested, second executed obliviously. Experiments give strong evidence that have structure. Proving property left as open problem.