Generalized Ware-Amdhal Law

We herein briefly describe a multilevel approach to analyze parallel algorithms performances. The main outcome of such an approach is that the algorithm is described using a set of operators related to each other according to the problem decomposition. A set of block matrices (called decomposition and execution matrices) highlights fundamental characteristics of the algorithm, such as inherent parallelism and sources of overheads, and all the involved factors and their relationships, in a general but modular, flexible and adaptive fashion. The work aims to show how we can rewrite the well-known Ware-Amdhal's Law: in a previous work we already gave an expression for the Amdhal's law in our framework, but, even with the same meaning, it wasn't immediately comparable with the original one. Here we focus on that law and show how it comes exactly from our parameters. Moreover, we extend the law with a more general expression, that we call Generalized Amdhal's Law: the classical law will come as a particular case of the generalized one.