Symbol T
T is part of the quantity the equation computes from the expression on the right.
Read this term in its guide →Published equation contexts
Why this formula appears here
The classical accounting for a collective operation separates three terms: a per-message latency, a per-byte transfer cost, and a per-byte computation cost for reductions [ 2 ] . Writing for latency per message, for transfer time per byte and for reduction time per byte, the cost of a collective over p participants on n bytes takes the shape . where L counts message steps, W counts bytes crossing each link and C counts arithmetic. The whole art of collective algorithm design is choosing which of these terms to pay.
Read the representative guide
Symbol n
n is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
Read this term in its guide →Symbol p
p is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
Read this term in its guide →Symbol L
L is one of the signed contributions combined to compute the quantity on the left.
Read this term in its guide →Symbol β
β is one of the signed contributions combined to compute the quantity on the left.
Read this term in its guide →Symbol W
W is one of the signed contributions combined to compute the quantity on the left.
Read this term in its guide →Symbol gamma
gamma is one of the signed contributions combined to compute the quantity on the left.
Read this term in its guide →Symbol C
C is one of the signed contributions combined to compute the quantity on the left.
Read this term in its guide →How to interpret it
Read it with the definitions, units, and assumptions supplied by the article.
Research cited beside this formula
Published contexts (1)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 9 · AI Hardware & Semiconductors
The Network Is the Computer Again
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
The classical accounting for a collective operation separates three terms: a per-message latency, a per-byte transfer cost, and a per-byte computation cost for reductions [ 2 ] . Writing for latency per message, for transfer time per byte and for reduction time per byte, the cost of a collective over p participants on n bytes takes the shape . where L counts message steps, W counts bytes crossing each link and C counts arithmetic. The whole art of collective algorithm design is choosing which of these terms to pay.