Break-even reuse count

Worked examples, recomputed

Every number the mechanisms quote for this relationship is recomputed from it, so none of them disagrees with it.

• 50 ms compile ÷ 20 ns saved per row → 2.5 million rows
• $65 to build, refresh and store ÷ $0.50 saved → 130 queries a month
• 2 TB kept a year: $552 against 4 × $60 = $240 to recompute

Where it appears

Each mechanism states it in its own names. The general symbol each name stands for is shown with it.

• Core Data Structures

  How do we choose a data structure when the real cost is set by the hardware, not by Big-O?

  $$\text{queries needed}=\text{sort\_cost}÷\text{saving\_per\_query}$$

  sort_cost = $C_{\text{fixed}}$ · saving_per_query = $\Delta c$

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• Query Planning & Optimization

  How does a system choose a plan for a question when the facts that decide the best plan are unknown until the plan has run?

  $$n^{\ast }=C_{\text{compile}}/\Delta c$$

  C_compile = $C_{\text{fixed}}$ · Δc (saved per tuple) = $\Delta c$

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• Execution Engine Runtime

  Once a query plan is chosen, why does the machine still sit idle, and what does each mechanism of a query runtime pay to buy that idle time back?

  $$50\text{ms}÷20\text{ns}=2.5\text{million tuples}$$

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• Cost Mechanics

  What is metered, and what is the smallest increment you are charged for?

  $$N^{\ast }=\frac{B+R\times \text{changes}+S\times T}{\text{savings per query}}$$

  B + R × changes + S × T = $C_{\text{fixed}}$ · savings per query = $\Delta c$

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• Cost Mechanics

  What is metered, and what is the smallest increment you are charged for?

  $$\text{store if storage over the horizon}<\text{recompute cost}\times \text{expected needs}$$

  Read it in place →