Abstract
The parallel program schemata, introduced by Karp and Miller [1], are considered for an unbounded number of operations and their decidability, result for determinacy is extended to this case under certain restrictions on the nature of the conflicts. The work of Keller [2] on maximal parallelism is discussed and an alternative approach to this problem is proposed which leads to a simple and fast solution algorithm for the general scheduling problem for unbounded parallelism. In contrast to this the general scheduling problem for bounded parallelism is NP-complete as proven in Ullman [3].
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References
Karp, R.M. and Miller, R.E. Parallel program schemata. Journal of Computer and System Sciences, 3, 147–195 (1969).
Keller, R.M. Parallel program schemata and maximal parallelism. Journal of the ACM, 20, 514–537 and 696–710 (1973).
Ullman, J.D. NP-complete scheduling problems. Journal of Computer and System Sciences, 10, 384–393 (1975).
Aho, A.V., Hopcroft, J.E. and Ullman, J.D. The Design and Analysis of Computer Algorithms. Reading, Mass. (1974).
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Gati, G. (1977). Aspects of unbounded parallelism. In: Theoretical Computer Science. Lecture Notes in Computer Science, vol 48. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08138-0_25
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DOI: https://doi.org/10.1007/3-540-08138-0_25
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