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Equation 9 · Part 10 · The Network Is the Computer Again

=

T(n,p)=α L(p)+β W(n,p)+γ C(n,p),T(n,p) = \alpha\,L(p) + \beta\,W(n,p) + \gamma\,C(n,p),
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

The classical accounting for a collective operation separates three terms: a per-message latency, a per-byte transfer cost, and a per-byte computation cost for reductions [ 2 ] . Writing α\alpha for latency per message, β\beta for transfer time per byte and γ\gamma for reduction time per byte, the cost of a collective over p participants on n bytes takes the shape T(n,p)=α L(p)+β W(n,p)+γ C(n,p)T(n,p) = \alpha\,L(p) + \beta\,W(n,p) + \gamma\,C(n,p). where L counts message steps, W counts bytes crossing each link and C counts arithmetic. The whole art of collective algorithm design is choosing which of these terms to pay.

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.