Hi,
With current master (8785ea0) I made some tests on a MySQL 5.5.37 server
containing about 81000 databases and about 81000 users.
In the mysql.db tables there are about 81000 grant entries; each one
grants some wildcard access to databases starting with a certain pattern.
I tested with root, since the reports we got about the server being slow
seem to be occurring for root.
Good news
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First, the login. It takes about 7 seconds before seeing the initial
page after login.
In the navi panel, there is a db page selector with 107 page numbers.
Going to any page takes about 7 seconds. Opening a db takes about 4
second (each db seems to contain about 31 tables).
Browsing tables, grid editing, searching inside a table behave normally.
Using Server > Databases works correctly, including switching pages.
Problems
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Going to a MyISAM table, Structure, and trying to change a column's
structure takes 30 seconds before seeing the dialog for this column.
Switching this table to InnoDB does not help.