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Equation 24 · Part 1 · The Network Is the Computer Again

Symbol T_rd

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),
TrdT_{\mathrm{rd}}

What this part means

TrT_rd is part of the quantity the equation computes from the expression on the right.

Its job in the formula

TrT_rd is part of the quantity the equation computes from the expression on the right.

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 subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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