In this report we describe a greedy algorithm to schedule parallel jobs that consist of independent, identical, compute-bound tasks on desktop grids that consist of volatile compute resources. We assume that the algorithm has full knowledge of future resource availability and we prove that it achieves the optimal schedule (i.e., the one with the minimum makespan). Although this algorithm cannot be implemented in practice, it is a good comparator to evaluate other scheduling heuristics and the makespan it achieves can be computed in a straightforward manner.
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