Abstract
This paper addresses the problem of optimally scheduling a cyclic set of interdependent operations (or tasks), representing for instance a program loop. While the existence of optimum periodic schedules has been demonstrated when processors are plentiful, the corresponding problem when the number of available processors is fixed, remains unanswered. In this work we show that if the operations' dependence graph is strongly connected, then there exists a p-processor optimum schedule, for any p, which is expressible in the form of a loop. To prove this result we have established a general pumping lemma for p-processor schedules akin to the classical pumping lemma for regular languages.
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© 1995 Springer-Verlag Berlin Heidelberg
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Gasperoni, F., Schwiegeishohn, U., Turek, J. (1995). Optimal loop scheduling on multiprocessors: A pumping lemma for p-processor schedules. In: Malyshkin, V. (eds) Parallel Computing Technologies. PaCT 1995. Lecture Notes in Computer Science, vol 964. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60222-4_96
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DOI: https://doi.org/10.1007/3-540-60222-4_96
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