Abstract
The paper classifies the problems solvable very fast in parallel with a feasible number of processors and contrasts them with problems hard to parallelize. The notions of NC1-reducibilities, RNC1-reducibilities, log-space reducibilities are presented and problems complete (or randomly complete) for P are defined and discussed. The notion of optimal parallel time-number of processors tradeoff is highlighted and several techniques to achieve optimal tradeoff are presented. Several results about fast parallel approximations to P-complete problems are described. Finally, certain milestones in the design of efficient parallel algorithms are noted and their impact is discussed.
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Spirakis, P.G. (1989). Fast parallel algorithms and the complexity of parallelism (basic issues and recent advances). In: Wolf, G., Legendi, T., Schendel, U. (eds) Parcella '88. Parcella 1988. Lecture Notes in Computer Science, vol 342. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50647-0_110
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