Online Scheduling with Bounded Migration

Consider the classical online scheduling problem where jobs that arrive one by one are assigned to identical parallel machines with the objective of minimizing the makespan. We generalize this problem by allowing the current assignment to be changed whenever a new job arrives, subject to the constraint that the total size of moved jobs is bounded by � times the size of the arriving job. Our main result is a linear time ‘online approximation scheme’, that is, a family of online algorithms with competitive ratio���� � and constant migration factor � ���� �, for any fixed�¤�� �. This result is of particular importance if considered in the context of sensitivity analysis: While a newly arriving job may force a complete change of the entire structure of an optimal schedule, only very limited ‘local ’ changes suffice to preserve near-optimal solutions. We believe that this concept will find wide application in its own right. We also present simple deterministic online algorithms with migration factors��� � and�� � ���� � , respectively. Their competitive ratio���� � beats the lowe