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Abstract: In this paper, we assess the impact of heterogeneity on scheduling independent tasks on master-slave platforms. We assume a realistic one-port model where the master can communicate with a single slave at any time. We target both on-line and off-line scheduling problems, and we focus on simpler instances where all tasks have the same size. While such on-line problems can be solved in polynomial time on homogeneous platforms, we show that there does not exist any optimal deterministic algorithm for heterogeneous platforms. Whether the source of heterogeneity comes from computation speeds, or from communication bandwidths, or from both, we establish lower bounds on the competitive ratio of any deterministic algorithm. We provide such bounds for the most important objective functions: the minimization of the makespan (or total execution time), the minimization of the maximum response time (difference between completion time and release time), and the minimization of the sum of all response times. Altogether, we obtain nine theorems which nicely assess the impact of heterogeneity on on-line scheduling. For off-line scheduling, we prove several result for problems with release dates, either optimality or NP-hardness. These theoretical contributions are complemented on the practical side by the implementation of several heuristics on a small but fully heterogeneous MPI platform. Our results show the superiority of those heuristics which fully take into account the relative capacity of the communication links. [Copyright &y& Elsevier]

In this paper, we discuss several algorithms for scheduling divisible workloads on heterogeneous systems. Our main contributions are (i) new optimality results for single-round algorithms and (ii) the design of an asymptotically optimal multi-round algorithm. This multi-round algorithm automatically performs resource selection, a difficult task that was previously left to the user. Because it is periodic, it is simpler to implement, and more robust to changes in the speeds of the processors and/or communication links. On the theoretical side, to the best of our knowledge, this is the first published result assessing the absolute performance of a multi-round algorithm. On the practical side, extensive simulations reveal that our multi-round algorithm outperforms existing solutions on a large variety of platforms, especially when the communication-to-computation ratio is not very high (the difficult case). [Copyright &y& Elsevier]