How can I in constant time (or closest possible) find the maximum or minimum value on an indexed column in an Mnesia table?
I would do it outside the Mnesia database. Keep an explicit-min and explicit-max by having a process which learns about these values whenever there is an insert into the table. This gives you awfully fast constant time lookup on the values.
If you can do with O(lg n) time then you can make the table an ordered_set. From there, first/1 and last/1 should give you what you want, given that the key contains the thing you are ordering by. But this also slows down other queries in general to O(lg n).
A third trick is to go by an approximate value. Once in a while you scan the table and note the max and min values. This then materializes into what you want, but the value might not be up to do date if it was a long time since you last scanned.