Equation 5 · Part 2 · How AI Datacenter Interconnects Actually Work
Symbol p
What this part means
the rather than growing with.
Its job in the formula
p is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol p→Article meaning
Where the article explains it
The total data volume any one worker sends over the whole operation is: V = 2(p-1) 2S p which is the reason ring all-reduce is called bandwidth-optimal: in the limit, total traffic per worker approaches twice the buffer size regardless of how many workers participate, rather than growing with p .
The passage around this formula
The ring algorithm is the one worth understanding 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 worker sends over the whole operation is:
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
These citations provide research context; check each source for the exact claim it supports.