Summary
Given a multiprocessor system consisting of M identical processors. Given N tasks and precedence rules for the execution of these tasks, represented as a finite, weighted forest G (whose paths are directed from leaves to roots). Given finally an upper bound T > 0 for the total processing time of G by the M processors. We assume that preemptions are allowed.
In an elementary way for this model 1) precise lower bounds Tmin(G;M) and Mmin(G;T) are developed: 2) and for T ≥ Tmin(G;M) or M ≥ Mmin(G;T) the ‘admissible’ processor assignments and their maximal running times are derived, and 3) the structure and therefore the set of all schedules is described that lead to complete processing of all tasks of G by M processors within time T.
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Schindler, S. (1973). Classes of Optimal Schedules for Multiprocessor Systems. In: Deussen, P. (eds) GI. Gesellschaft für Informatik e.V. 2. Jahrestagung. Lecture Notes in Economics and Mathematical Systems, vol 78. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80732-9_25
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DOI: https://doi.org/10.1007/978-3-642-80732-9_25
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