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In this paper we consider the power of migration in heterogeneous machines settings and general profit scheduling. We begin by showing that on related machines or on related machines with restricted assignment that any migratory algorithm can be simulated by a non-migratory algorithm given 1+ε speed augmentation and O(1/ε) and O(1/ε2) machine augmentation, respectively, for any 0 i(t) specifying the profit of completing job i at time t. The goal of the schedule is to maximize the total profit obtained. We give a (1+ε)-speed O(1/ε2)-competitive algorithm in the unrelated machines setting for any ε >0 when compared against a non-migratory adversary. Previous results were only known in the identical machines setting. As an example of the usefulness of the previous results on migration, they with the results on genial profit scheduling give a (1+ε)-speed O(1/ε4)-competitive algorithm for general profit scheduling when comparing against a migratory algorithm on related machines with restricted assignment for any ε >0.

General Profit Scheduling and the Power of Migration on Heterogeneous Machines