On effective procedures for speeding up algorithms

Authors:
Manuel Blum
Affiliations:
Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California
Venue:
STOC '69 Proceedings of the first annual ACM symposium on Theory of computing
Year:
1969

Citing 2
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Abstract

This paper is concerned with the nature of speedups. Let f be any recursive function. We show that there is no effective procedure for going from an algorithm for f to a significantly faster algorithm for f. On the other hand, there is an effective procedure for going from any algorithm to a faster algorithm, provided one has a bound on the size of the algorithm that does the computation faster for all inputs. If no bound on the size of the faster algorithm is known in advance, one can still obtain a pseudo speedup: This is a very fast algorithm which computes a variant of the function, one which differs from the original function on a finite number of inputs.