Equation 14 · The Network Is the Computer Again
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol n
n is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Symbol p
p is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
How to interpret it
Read this expression with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
Consider the two canonical all-reduce algorithms. A ring arranges participants in a cycle and performs a reduce-scatter followed by an all-gather, each in p-1 steps carrying n/p bytes:
Sources cited in the article section
- [2] Collective communication: theory, practice, and experience ↗
- [3] NCCL Tests — Performance Reporting and Bus Bandwidth ↗
- [1] Optimization of Collective Communication Operations in MPICH ↗
These citations give research context. Read each source to check which claims it supports.
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