Whatsonyourmind commented on issue #21120:
URL: https://github.com/apache/datafusion/issues/21120#issuecomment-4182731153
A few notes on the Selinger-style default analyzer for the planned work:
For **selectivity estimation** of comparison predicates (`col > const`), the
classic approach when histograms are unavailable is the uniform distribution
assumption with min/max bounds:
```
selectivity(col > c) = (max - c) / (max - min) when min ≤ c ≤ max
selectivity(col > c) = 0 when c > max
selectivity(col > c) = 1 when c < min
```
For compound predicates, the independence assumption gives:
- `AND`: multiply selectivities
- `OR`: `1 - (1 - s1)(1 - s2)`
- `NOT`: `1 - s`
For **NDV propagation through expressions**: arithmetic operations like `col
+ 1` preserve NDV exactly. For `col1 + col2`, the upper bound on NDV is
`min(NDV1 * NDV2, row_count)`. For functions like `FLOOR(col)`, NDV can only
decrease: `NDV_out ≤ NDV_in`. For `date_trunc('month', ts_col)`, NDV can be
estimated as `(max - min) / interval_size`.
One design consideration: the chain-of-responsibility pattern should
propagate **confidence levels** alongside estimates. A histogram-based analyzer
might return `(selectivity=0.23, confidence=High)`, while a fallback heuristic
returns `(selectivity=0.20, confidence=Low)`. The optimizer can then weight its
cost model decisions by confidence -- preferring plans that are robust to
estimation error when confidence is low.
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