I'm looking at the name of a variant of the Stable Roommates Problem, when the rooms have more than 2 mates, ie for example 6 to 8. Does this problem has a specific name? A well-known algorithm?
To summarize, the problem is the following: Given a set of $n$ people, and a symetric $n\times n$ affinity matrix between each person, find an optimal disjoint set partition of the people into $m$ groups of a given size, maximizing the global "affinity score" (the sum of each pair affinity in each group).
Why this question? I'm organizing a wedding ceremony with around 60 people, grouping people into tables of 6 to 8. Each person pair has an affinity weight, ranging from $-\infty$ (they can't stand each other) to $+\infty$ (they better be together).
This question is somehow related, but unfortunatly does not have any answer.