# How to cluster similar objects into fixed size groups?

I have $n$ people each of which can meet on certain days of the week. I want to group them into $\frac{n}{k}$ groups of size $k$ such that all people in a group can meet on a day.

eg - Suppose there are 3 people who are free on (M,T,W,Th,F), (M,W) and (W,Th,F) respectively. They can all be placed in the same group since all of them can meet on Wednesday.

• @PålGD Edited and made it simpler. – ask Jun 11 '15 at 16:19
• Superpositions are allowed? – André Souza Lemos Jun 11 '15 at 16:36
• It's probably NP-hard. Check out set cover. Or maybe red-blue dominating set on bipartite graphs? With days on one side and people on the other side of the bipartition? – Pål GD Jun 11 '15 at 16:36