Improved approximation schemes for scheduling unrelated parallel machines
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Approximating Scheduling Unrelated Parallel Machines in Parallel
Computational Optimization and Applications
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We present a general framework for approximation schemes on parallel processor scheduling. We propose e-approximation algorithms for scheduling on identical, uniform and unrelated machines when the number of processors is fixed. For each of the three problems considered, we perform grouping on job processing times in order to produce a transformed scheduling instance where the number of distinct task types is bounded. We optimally solve the corresponding mixed integer program and we prove that the optimal makespans for the initial and the transformed problems can differ at most by a factor of 1+e. The complexity of all e-approximation algorithms is O(n), where n is the number of jobs to be scheduled.