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Equation 24 · Part 3 · The Network Is the Computer Again

Symbol p

Trd(n,p)=⌈log⁡2p⌉ α+⌈log⁡2p⌉ n (β+γ),T_{\mathrm{rd}}(n,p) = \lceil \log_2 p \rceil \,\alpha + \lceil \log_2 p \rceil \, n\,(\beta + \gamma),
pp

What this part means

p is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Its job in the formula

p is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

The passage around this formula

But look at the latency term: 2(p-1)α\alpha grows linearly in the number of participants. A recursive-doubling or tree scheme instead completes in ⌈\lceil log⁡2\log_2 p ⌉\rceil rounds: Trd(n,p)=⌈log⁡2p⌉ α+⌈log⁡2p⌉ n (β+γ)T_{\mathrm{rd}}(n,p) = \lceil \log_2 p \rceil \,\alpha + \lceil \log_2 p \rceil \, n\,(\beta + \gamma). paying a logarithmic latency term but sending the full message in every round, so its bandwidth cost grows with log⁡\log p rather than staying flat.

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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 article section

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