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The Sun-Ni law is an approach used in parallel processing that attempts to improve performance. It is also called memory bounded speedup and was proposed by Professors Xian-He Sun and Lionel M. Ni. This law scales up the problem size and tries to find a solution limited only by the amount of memory available. It is a generalization of two other approaches used in parallel computing called Amdahl's law and Gustafson's law.
One of the challenges in parallel computing is to figure out how the performance of the system improves when it is scaled up. As this can be hard to measure, one of the most well-known scalability metrics studied is speedup. Speedup relates the execution of parallel programs running on a certain number of processors and the execution time it takes for the fastest sequential program to solve that problem. One type of speedup approach is to keep the problem size constant, allowing the number of processors that work on the problem to be increased. This is called Amdahl's law and is known as fixed-size speedup.
Amadhl's law thus attempts to reduce the execution time using more parallel processors and fixes the computational workload as a constant. It essentially tries to solve the problem in lesser and lesser time. In contrast, Gustafson's law, also known as fixed-time speedup, tries to obtain a result within a fixed time and scales up the problem size, carrying out more operations to get an accurate solution. This is applied to problems where there is a time constraint, but it is not vital to solve them in the shortest possible time.
The memory bounded speedup approach, or the Sun-Ni law, is concerned with memory size and how it affects performance. The problem size that can be tackled is affected by the amount of memory available. A limited physical memory means that more time is spent figuring out workarounds to solve a problem within the parallel computing architecture. The approach the Sun-Ni law takes is, if the time limit specified by the fixed-time speedup is met and there is enough memory space, the problem should be scaled to make adequate use of all the available memory.
This is what the Sun-Ni law does, and the formula considers memory size and relates it to performance. Every processor in a parallel computing architecture has a fixed memory, and the formula relates the problem size to the total available memory capacity. The memory bounded speedup laid out in the Sun-Ni law is, in essence, a generalization of both the fixed-time and fixed-size speedups. Given that the total memory size increases when the number of processors increase, the Sun-Ni law attempts to utilize all that memory space more efficiently.