Brent’s Theorem

Synonyms

Brent’slaw

Definition

Assume a parallel computer where each processor can perform an arithmetic operation in unit time. Further, assume that the computer has exactly enough processors to exploit the maximum concurrency in an algorithm with N operations, such that T time steps suffice. Brent’s Theorem says that a similar computer with fewer processors, P, can perform the algorithm in time

$${T}_{P} \leq T + \frac{N - T} {P},$$

where P is less than or equal to the number of processors needed to exploit the maximum concurrency in the algorithm.

Brent’s Theorem. Fig. 1

Concurrency of a solver for two equations in two unknowns