Linear time approximation schemes for parallel processor scheduling

The authors present a general framework for approximation schemes on parallel processor scheduling. They propose ε-approximation algorithms for scheduling on identical, uniform and unrelated machines when the number of processors is fixed. For each of the three problems considered, they perform grouping on job processing times in order to produce a transformed scheduling instance where the number of distinct task types is bounded. They optimally solve the corresponding mixed integer program and prove that the optimal makespans for the initial and the transformed problems can differ at most by a factor of 1+ε The complexity of all ε-approximation algorithms is O(n), where n is the number of jobs to be scheduled