Self-similarity of parallel machines

Self-similarity is a property of physical systems that describes how to scale parameters such that dissimilar systems appear to be similar. Computer systems are self-similar if certain ratios of computational forces, also known as computational intensities, are equal. Two machines with different computational power, different network bandwidth and different inter-processor latency behave the same way if they have the same ratios of forces. For the parallel conjugate gradient algorithm studied in this paper, two machines are self-similar if and only if the ratio of one force describing latency effects to another force describing bandwidth effects is the same for both machines. For the two machines studied in this paper, this ratio, which we call the mixing coefficient, is invariant as problem size and processor count change. The two machines have the same mixing coefficient and belong to the same equivalence class.

Research highlights
► We apply dimensional analysis to a performance model for a parallel conjugate gradient algorithm.
► We observe that a quantity called the mixing coefficient is invariant.
► Machines with the same value of the mixing coefficient belong to the same equivalence class.