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A polynomial-time algorithm is presented for partitioning a collection of sporadic tasks, each constrained to have its relative-deadline parameter be no larger than its period parameter, among the processors of an identical multiprocessor platform. Since the partitioning problem is easily seen to be NP-hard in the strong sense, this algorithm is unlikely to be optimal. A quantitative characterization of its worst-case performance is provided in terms of resource augmentation. It is shown that any set of sporadic tasks that can be partitioned among the processors of an m-processor identical multiprocessor platform will be partitioned by this algorithm on an m-processor platform in which each processor is (3-(1/m)) times as fast.