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Consider the problem of determining a task-to-processor assignment for a given collection of implicit-deadline sporadic tasks upon a multiprocessor platform in which there are two distinct kinds of processors. We propose a polynomial-time approximation scheme (PTAS) for this problem. It offers the following guarantee: for a given task set and a given platform, if there exists a feasible task-to-processor assignment, then given an input parameter, e, our PTAS succeeds, in polynomial time, in finding such a feasible task-to-processor assignment on a platform in which each processor is 1+3e times faster. In the simulations, our PTAS outperforms the state-of-the-art PTAS and also for the vast majority of task sets, it requires significantly smaller processor speedup than (its upper bound of) 1+3e for successfully determining a feasible task-to-processor assignment.