Perfect Strong Scaling Using No Additional Energy

Energy efficiency of computing devices has become a dominant area of research interest in recent years. Most previous work has focused on architectural techniques to improve power and energy efficiency; only a few consider saving energy at the algorithmic level. We prove that a region of perfect strong scaling in energy exists for matrix multiplication (classical and Strassen) and the direct n-body problem via the use of algorithms that use all available memory to replicate data. This means that we can increase the number of processors by some factor and decrease the runtime (both computation and communication) by the same factor, without changing the total energy use.