Abstract
Speeding up automatically means to find a parallel algorithm for an arbitrary sequential one, so that the time for designing this parallel algorithm plus its runtime is considerably lower than the time sequentially used. Here we consider sequential and parallel random access machines (RAMs, PRAMs) with arithmetic instructions {+, −, *}. RAMs work on integer inputs and use direct and a restricted form of indirect addressing, only.
We extend the result of Meyer auf der Heide ([MEYE86]) to RAMs which can also multiply. We use techniques for fast parallel computation of polynomials due to Valiant, Skyum, Berkowitz and Rackoff ([VSBR83]). In order to apply this we have to make their simulation uniform. This result, interesting in itself, is based on an efficient parallelization of straight-line programs with operations {+,max}.
With a PRAM with a processors we gain a speed up factor of \(\frac{{(log log q)^2 + log log q \cdot log D}}{{log q}}\)for any uniform RAM P, where D denotes the formal degree of the polynomials computed by P.
Work supported by the Deutsche Forschungsgemeinschaft, grants No. ME 872/1-1
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References
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© 1988 Springer-Verlag Berlin Heidelberg
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Wald, I. (1988). An automatic speed-up of random access machines with powerful arithmetic instructions. In: Cori, R., Wirsing, M. (eds) STACS 88. STACS 1988. Lecture Notes in Computer Science, vol 294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035837
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DOI: https://doi.org/10.1007/BFb0035837
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