A generalization of Amdahl's law and relative conditions of parallelism

Abstract

In this work I present a generalization of Amdahl's law on the limits of a parallel implementation with many processors. In particular I establish some mathematical relations involving the number of processors and the dimension of the treated problem, and with these conditions I define, on the ground of the reachable speedup, some classes of parallelism for the implementations. I also derive a condition for obtaining superlinear speedup. The used mathematical technics are those of differential calculus. I describe some examples from classical problems offered by the specialized literature on the subject.