Amdahl\u27s Law states that speedup in moving from one processor to N identical processors can never be greater than N, and in fact usually is lower than N because of operations that must be done sequentially. Amdahl\u27s Law gives us the following formula for speedup: Speedup \u3c or = (S+P)/(S+(P/N)) where is the number of processors, S is the percentage of the code that is serial (i.e., cannot be parallelized), and P is the percentage of code that is parallelizable. We can substitute 1 - S for P in the above formula and we see that as S approaches zero speedup approaches N. It can also be shown that seemingly small values of S can severely limit the maximum speedup. Researchers at the University of Maine saw speedups that seemed to contradict Amdahl\u27s Law, and identified an assumption made by the law that is not always true. When this assumption is not true, it is possible to achieve speedups that are larger than the theoretical maximum speedup of N given by Amdahl\u27s Law. The assumption in question is that the computer performance scales linearly as the size of the problem is reduced by dividing it over a larger number of processors. This assumption is not valid for computers with tiered memory. In this thesis we investigate superlinear speedup through a series of test programs specifically designed to exhibit superlinear speedup. After demonstrating these programs show superlinear speedup, we suggest methods for detecting the potential for superlinear speedup in a variety of algorithms
