Equation 15 · Part 12 · The Network Is the Computer Again
Numerator: 2(p-1)
What this part means
The complete quantity above the fraction bar.
Its job in the formula
2(p-1) occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Full expression→Numerator: 2(p-1)→Article meaning
The passage around this formula
…own performance documentation encodes exactly this factor, defining the bus bandwidth of an all-reduce by applying a correction of 2(p-1)/p to the naive size-over-time figure, on the reasoning that an all-reduce requires 2(p-1) data transfers across p links; all-gather, reduce-scatter and all-to-all get a factor of (p-1)/p , while broadcast and reduce get a factor of one because everything must pass through a single root [ 3 ] . The point of the correction is that bus bandwidth should stay roughly constant as ranks…
Learn the underlying idea
A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.
Open the illustrated fractions: division written vertically guide →
Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.