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Abstract. This paper considers the problem of minimizing the schedule length of a two-machine shop in which notonly can a job be assigned any of the two possible routes, but also the processing times depend on the chosen route.This problem is known to be NP-hard. We describe a simple approximation algorithm that guarantees a worst-caseperformance ratio of 2. We also present some modifications to this algorithm that improve its performance andguarantee a worst-case performance ratio of 3=2.
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