Abstract
Preemptive scheduling problems of minimizing the makespan on parallel machines are basic problems. Motivated by sensitivity analysis and online algorithms, we investigate the problem of designing robust algorithms that are faced with the input one job at a time, but unlike online algorithms they are allowed to modify a small portion of the solution whenever a new job is released. For the settings of uniformly related machines, it is known that such algorithms cannot maintain an optimal solution (for general input sequences). Thus, we consider the semi-online case where the job sequence has non-increasing job sizes and design an optimal algorithm with migration factor 1. Previously such result was known only for the case of identical machines where it holds for an arbitrary input sequence.
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