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Equation 6 · Part 3 · How AI Datacenter Interconnects Actually Work

Symbol S

V=2(p−1)⋅Sp≈2Sfor large pV = 2(p-1)\cdot\frac{S}{p} \approx 2S \quad \text{for large } p
SS

What this part means

S occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Its job in the formula

S occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

…mechanically, because it is bandwidth-optimal and because its cost model exposes exactly why topology matters. In a ring all-reduce across p workers, each worker is logically placed on a ring; a gradient buffer of size S is split into p chunks, and each worker simultaneously sends one chunk to its ring-neighbor while receiving a different chunk from its other neighbor, reducing (summing) as chunks arrive. A complete all-reduce takes 2(p-1) such steps, each moving S/p bytes [ 5 ] . The total data volume any one…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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