Re: Implement missing join selectivity estimation for range types

Hello Mahmoud,

Thanks for the patch and sorry for not taking a look earlier.

On 6/30/22 16:31, Mahmoud Sakr wrote:
> Hi,
> Given a query:
> SELECT * FROM t1, t2 WHERE t1.r << t2.r
> where t1.r, t2.r are of range type,
> currently PostgreSQL will estimate a constant selectivity for the << predicate,
> which is equal to 0.005, not utilizing the statistics that the optimizer
> collects for range attributes.
> 
> We have worked out a theory for inequality join selectivity estimation
> (http://arxiv.org/abs/2206.07396), and implemented it for range
> types it in this patch.
> 

Interesting. Are there any particular differences compared to how we
estimate for example range clauses on regular columns?

> The algorithm in this patch re-uses the currently collected statistics for
> range types, which is the bounds histogram. It works fairly accurate for the
> operations <<, >>, &&, &<, &>, <=, >= with estimation error of about 0.5%.

Right. I think 0.5% is roughly expected for the default statistics
target, which creates 100 histogram bins, each representing ~1% of the
values. Which on average means ~0.5% error.

> The patch also implements selectivity estimation for the
> operations @>, <@ (contains and is contained in), but their accuracy is not
> stable, since the bounds histograms assume independence between the range
> bounds. A point to discuss is whether or not to keep these last two operations.

That's a good question. I think the independence assumption is rather
foolish in this case, so I wonder if we could "stabilize" this by making
some different - less optimistic - assumption. Essentially, we have an
estimates for lower/upper boundaries:

  P1 = P(lower(var1) <= lower(var2))
  P2 = P(upper(var2) <= upper(var1))

and independence means we take (P1*P2). But maybe we should be very
pessimistic and use e.g. Min(P1,P2)? Or maybe something in between?

Another option is to use the length histogram, right? I mean, we know
what the average length is, and it should be possible to use that to
calculate how "far" ranges in a histogram can overlap.

> The patch also includes the selectivity estimation for multirange types,
> treating a multirange as a single range which is its bounding box.
> 

OK. But ideally we'd cross-check elements of the two multiranges, no?

> The same algorithm in this patch is applicable to inequality joins of scalar
> types. We, however, don't implement it for scalars, since more work is needed
> to make use of the other statistics available for scalars, such as the MCV.
> This is left as a future work.
> 

So if the column(s) contain a couple very common (multi)ranges that make
it into an MCV, we'll ignore those? That's a bit unfortunate, because
those MCV elements are potentially the main contributors to selectivity.


regards

-- 
Tomas Vondra
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