From 4. Conclusion

the above equation, we can see that we will get the best performance if we choose a blocking factor that is a multiple of 3. In general, the theorem implies that there are only blocking factors to consider; this characterizes the critical path for all unfoldings greater than. In this paper, we have developed a formulation for the problem of finding optimal blocking factors for blocked, non-overlapped schedules. We have used a max-algebra formulation to show that the critical path in a-unfolded HSDF graph becomes cyclic as becomes large enough. We have shown that it is possible to determine this cyclic-ity by analyzing the critical graph of the-matrix, a matrix that arises out of the model. The cyclicity of the critical path implies that we have to examine only a finite number of unfoldings to determine whether a rate-optimal unfolding exists. This number is equal to the sum of the cyclicity and a transient. While this paper has contributed to our theoretical understanding of the dynamics of increasing the blocking factor when there are no processor or communication constraints, finding the optimal blocking factor under those constraints is still an open problem. The results in this paper certainly give us a technique to determine upper bounds on the performance we can expect when these constraints are present.