How can I mathematically figure out which 'sets' of reports can be assigned to people instead of individual user<->report rules so that I have some efficient groups and long-term administration becomes a bit easier?

It depends. :-) You could think up an algorithm that determines the current grouping according to the table, but chances are that that grouping won't be consistent in the long run. My guess is that you'll be better off if you try to find "logical" groups, possibly creating a few more reports for some people (i.e. put people in groups that have all the reports they need plus maybe one or two that they don't).

Look at it this way: If you don't group people, you have 100 groups (1 for each report). If you try to minimize the amount of groups, you might end up with groups that don't make any sense (and thus need a lot of maintenance).

I'd probably go for some mechanism that allows me to tweak the groups manually, starting with a few obvious groups (like the Accounts group) and some additional small groups to make up for the reports that don't match well. Depending on the exact data, that might cut down the amount of time spent on managing the reports by 80% or so.

Just a thought.