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Equation 24 · Part 6 · The Network Is the Computer Again

Symbol gamma

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),
γ\gamma

What this part means

gamma is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

gamma is one of the signed contributions combined to compute the quantity on the left.

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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