Equation 10 · Part 1 · 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
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
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 . What does grow with p is the number of sequential steps, 2(p-1) , and each step’s latency is bounded below by the slowest link and the slowest worker in the ring — which is precisely why NCCL switches to a tree algorithm for smaller messages and larger worker counts, trading some bandwidth…
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.