Gustafson's law

A model of parallel computing that predicts speedup as processor count grows when total execution time is fixed by scaling the problem size.

Gustafson's law equation: The relation S(P) = P − α(P − 1), estimating speedup for P processors and serial fraction α. The equation makes the law’s fixed-time scaling assumption explicit.
Amdahl's law: A model of parallel speedup that limits gains when a fixed fraction of a workload remains serial. It holds problem size fixed, unlike Gustafson’s scaling assumption.
John L. Gustafson: An American computer scientist who formulated the scaled-speedup argument in parallel computing. He introduced the law in a 1988 paper challenging Amdahl’s framing.
Scientific computing: The use of computation to model, analyze, and solve problems in scientific research. Scientific workloads often grow in detail as parallel resources become available.
Serial fraction: The fraction of a computation that must execute sequentially rather than concurrently. It limits the speedup predicted by Gustafson’s model.
Strong scaling: The study of how execution time changes as more processors solve the same fixed-size problem. It describes the fixed-work regime that Gustafson’s law contrasts with.
Amdahl's 1967 paper: Gene Amdahl’s paper arguing that serial work limits the benefits of parallel processing. Gustafson’s argument directly responds to its fixed-problem perspective.
High-performance computing: Computing systems designed to solve demanding problems using substantial processing and memory resources. Gustafson’s law helps frame expected gains on these systems.
Parallel fraction: The fraction of a computation whose operations can run concurrently. As the problem grows, this share can dominate the fixed execution time.
Weak scaling: The study of how execution time changes as problem size grows in proportion to processor count. It is the practical scaling regime closest to Gustafson’s fixed-time premise.

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