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 β times the size of the arriving job. For small values of β, we obtain several simple online algorithms with constant competitive ratio. We also present a linear time "online approximation scheme', that is, a family of online algorithms with competitive ratio 1+ε and constant migration factor β(ε), for any fixed ε>0