Amdahl’s Law

Amdahl’s Law reveals the maximum speedup that can be expected from parallel algorithms given the proportion of parts that must be computed sequentially. It gives the speedup $S$ as

$$S\le \frac{1}{f+(1-f)/N}$$

Where $f$ is the fraction of the problem that must be computed sequentially and $N$ is the number of processors.

Note that as $f$ approaches zero, $S$ nears $N$, which we’d expect from a perfectly parallelizable algorithm.