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.
Just model your problem with graph and use any of the widely known search algorithm to help traverse your graph. After doing that, if you have any problem, let us know.