I have similar situation like question below.
SELECT MAX(id) id, cid FROM table GROUP BY cid
To optimize above query (shown in the question), creating index(cid, id) does the trick.
However, when I add a column that is not indexed to SELECT, query speed drastically slows down.
For example,
SELECT MAX(id) id, cid, newcolumn FROM table GROUP BY cid
If I create index(cid, id, newcolumn), query time comes back to minimal. It seems I should index all the columns I select while using GROUP BY.
Is there any way other than indexing all the columns to be select?