Mariadb Building the best INDEX for a given SELECT - GROUP BY - indexing

Question

I do not have much knowledge in the database.
For study, I am reading MariaDB's index documents.
But there are parts that I do not understand.
Document
Algorithm, step 2b (GROUP BY)¶
WHERE aaa = 123 AND bbb = 1 GROUP BY ccc ⇒ INDEX(bbb, aaa, ccc) or INDEX(aaa, bbb, ccc) (='s first, in any order; then the GROUP BY)
aaa or bbb knows that ordering of the indexes is important, regardless of the order of the where clauses. Therefore, the indexes of aaa and bbb in the where clause are used, and sort ccc based on the matched aaa and bbb.
GROUP BY x,y ⇒ INDEX(x,y) (no WHERE)
(no WHERE) means don't use WHERE clause?
What if I use it like this?
WHERE x > 1 GROUP BY x, y
my think:
(1) from table
(2) where x > 1 -> using index
(3) group by x, y -> using index..? because (2) already sorted..? or sort again?
(4) having -> if i did not enter this keyword, is it not used?
(5) select -> print data(?)
(6) order by -> group by already order by(?)

Answer 1

Algorithm, step 2b (GROUP BY)¶
WHERE aaa = 123 AND bbb = 1 GROUP BY ccc ⇒ INDEX(bbb, aaa, ccc) or INDEX(aaa, bbb, ccc) (='s first, in any order; then the GROUP BY)
there is table like below:
aaa | bbb | ccc
------------------
123 | 1 | 30
------------------
123 | 1 | 48
------------------
123 | 2 | 27
------------------
125 | 1 | 11
------------------
125 | 3 | 29
------------------
125 | 3 | 40
------------------
WHERE aaa = 123 AND bbb = 1 clause result is this:
aaa | bbb | ccc
------------------
123 | 1 | 30
------------------
123 | 1 | 48
check ccc column.
ccc column is sorted by bbb column.
so GROUP BY clause can be grouped quickly because the ccc columns are sorted.
**CAUTION**
think about WHERE aaa >= 123 AND bbb = 1 GROUP BY ccc clause.
aaa | bbb | ccc
------------------
123 | 1 | 30
------------------
123 | 1 | 48
------------------
125 | 1 | 11
------------------
ccc column doesn't be sorted by bbb column.
The ccc column is meaningful only if the aaa and bbb columns have the same value.
GROUP BY x,y ⇒ INDEX(x,y) (no WHERE)
this is same thing.

Answer 2

GROUP BY x,y ⇒ INDEX(x,y) (no WHERE)
should probably say "(if there is no WHERE)". If there is a WHERE, then that index may or may not be useful. You should (usually) build the INDEX based on the WHERE, an only if you get past it, consider the GROUP BY.
WHERE x > 1 GROUP BY x, y
OK, that can use INDEX(x,y), in that order. First, it will filter, and that leaves the rest of the index still in a good order for the grouping. Similarly:
WHERE x > 1 ORDER BY x, y
WHERE x > 1 GROUP BY x, y ORDER BY x, y
No sorting should be necessary.
So, here are the steps I might take:
1. WHERE x > 1 ... --> INDEX(x) (or any index _starting_ with `x`)
2. ... GROUP BY x, y --> INDEX(x,y)
3. recheck that I did not mess up the WHERE.
This has no really good index:
WHERE x > 1 AND y = 4 GROUP BY x,y
1. WHERE x > 1 AND y = 4 ... --> INDEX(y,x) in this order!
2. ... GROUP BY x,y --> can use that index
However, flipping to GROUP BY y,x has the same effect (ignoring the order of display).
(4) having -> if i did not enter this keyword, is it not used?
HAVING, if present, is applied after things for which INDEXes are useful. Having no HAVING does mean there is no HAVING.
(6) order by -> group by already order by(?)
That has become a tricky question. Until very recently (MySQL 8.0; don't know when or if MariaDB changed), GROUP BY implied the equivalent ORDER BY. That was non-standard and potentially interfered with optimization. With 8.0, GROUP BY does not imply any order; you must explicitly request the order (if you care).
(I updated the source document in response to this discussion.)