6 Conclusion and Future Work

21 Like all other papers that have addressed this problem, the mappings generated by this strategy use a heuristic. Experimental evidence has been presented to justify the use of this heuristic, however, one aspect we want to examine further is a bound on the ratio of our mapping algorithm versus the optimal. This examination is useful both for quantifying the worst-case and expected results of the mapping algorithm, and for identifying potential renements to the heuristic. Many approaches, including our approach, rst cluster tasks and then map the clusters. We are convinced that these steps need to be integrated to nd a better solution to the general mapping problem. While clustering reduces the complexity of the mapping step, it needs to be made less architecturally independent. As discussed in Section 5, a trade-o exists between mapping critical clusters close together to decrease the transmission time of the critical edges, and mapping the critical clusters further apart to reduce bandwidth contention. This idea has potential for future research. Finally, we plan to study the restrictions previously mentioned that each task can begin execution only after it has received all the messages it needs and that it does not send any message until it has completed execution. We plan to consider the ramications of eliminating this requirement and the complexity of incorporating this change into our model. 20 not hold for the mapping algorithms that do not check the bandwidth contention. This is due to the fact that the best mapping is being chosen using inaccurate assumptions. Except for the smallest problem sizes, the random mapping algorithm has the worst performance. This is not surprising, since the probability that the random mapping generates an optimal mapping is inversely proportional to the number of processors. The variation between the results in this paper is much less than the variation given in [7]. The reason for this relatively limited variation is that packet switching is used. Message switching is used in [7]. Message switching is more sensitive than packet switching to the distance between processors. This results in increased overhead for sending messages between processors that are not directly connected. Since a random mapping is more likely to have critical edges that are not transmitted between directly connected processors, the communication overhead for the random mapping is signicantly higher for message switching than packet switching. Although our algorithm consistently nds a better mapping than …