/sci/ - Science & Math

>>12487940
>tfw when bad at mathematics but want to get a degree in applied maths
how do I cope with this

Pls help me /sci/, I'm retarded.

How do you find the largest partition of a set, given certain relations? By largest partition I mean the partition with most sets. With no restrictions this would be trivial, e.g. [1 2 3 4 5 6 7] gives [1] [2] [3] [4] [5] [6] [7]. But say you had relations like

1
2 ~ 4
3
4 ~ 6 7
5
6 ~ 4
7 ~ 4

So the partition with 2 must also contain 4, and 4 must also have 6 and 7, so the largest partition is [1] [2 4 6 7] [3] [5]. Is there an algorithm that can solve this without needing to loop n times or reach huge recursion depths (e.g. 1~2, 2~3, 3~4... would lead to a shitload of recursion)? Is this even a studied problem, and if so what do I need to search to read up on it? Is there a really simple algorithm I can't see because I'm retarded? Does it help if you can assume the given relations are symmetrical (but not transitive)?