Performance evaluation on multiprocessor task scheduling with resource augmentation

We study the worst-case performance of approximation algorithms for the problem of multiprocessor task scheduling on m identical processors with resource augmentation, whose objective is to minimize the makespan. In this case, the approximation algorithms are given k (k >= 0) extra processors than the optimal off-line algorithm. For on-line algorithms, the Greedy algorithm and shelf algorithms are studied. For off-line algorithm, we consider the LPT (longest processing time) algorithm. Particularly, we prove that the schedule produced by the LPT algorithm is no longer than the optimal off-line algorithm if and only if k >= m - 2.