Representing the scaling behavior of parallel algorithm-machine combinations

The scaling of algorithms and machines is essential to achieve the goals of high-performance computing. Thus, scalability has become an important aspect of parallel algorithm and machine design. It is a desirable property that has been used to describe the demand for proportionate changes in performance with adjustments in system size. It should provide guidance toward an optimal choice of an architecture, algorithm, machine size, and problem size combination. However, as a performance metric, it is not yet well defined or understood. The paper summarizes several scalability metrics, including one that highlights the behavior of algorithm-machine combinations as sizes are varied under an isospeed condition. A scaling relation is presented to facilitate general mathematical and visual techniques for characterizing and comparing the scalability information of these metrics