What’s the Sun-Ni law?

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The Sun-Ni law is an approach used in parallel computing that attempts to improve performance. It is also called memory-limited speedup and was proposed by professors Xian-He Sun and Lionel M. Ni. This law increases the size of the problem 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 understanding how system performance improves as it scales. Because it can be difficult to measure, one of the best-known scalability metrics studied is acceleration. Speedup relates the execution of parallel programs running on a certain number of processors to the execution time needed by the fastest sequential program to solve that problem. One type of approach to speeding up is to keep the problem size constant by allowing the number of processors working on the problem to grow. This is called Amdahl’s law and is known as a fixed size speedup.

Amadhl’s law then attempts to reduce the execution time by using multiple parallel processors and fixes the computational workload as a constant. In essence, try to solve the problem in less and less time. In contrast, Gustafson’s law, also known as fixed-time speedup, tries to get a result within a fixed time and scales the size of the problem, doing more things to get an accurate solution. This applies to problems where there is a time constraint, but it is not vital to solve them as quickly as possible.

The memory-limited acceleration approach, or Sun-Ni law, is concerned with the size of memory and how it affects performance. The size of the problem that can be addressed is affected by the amount of memory available. Limited physical memory means more time is spent looking for workarounds to solve a problem within the parallel computing architecture. The approach taken by the Sun-Ni law is that, if the time limit specified by fixed-time acceleration is met and there is sufficient memory space, the problem should be scaled to make adequate use of all available memory .

This is what the Sun-Ni law does, and the formula looks at memory size and relates it to performance. Each processor in a parallel processing architecture has fixed memory, and the formula relates the size of the problem to the total available memory capacity. The memory-limited acceleration predicted by the Sun-Ni law is, in essence, a generalization of both fixed-time and fixed-dimension acceleration. Since the total size of memory increases as the number of processors increases, the Sun-Ni law attempts to use all memory space more efficiently.

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