I'm having trouble to model the following as a max-flow problem.
Problem description. You have a group of N people. Each person belongs to one of the K teams. There are T tables with capacity of 6 people.
Is there a way to assign people to tables such as every team gets assigned to the same table?
My flow graph is
Nodes:
- nodes source (s) and sink (t)
- one node for each person
- one node for each team
- one node for each table
Edges:
- from source to person with capacity 1
- from person to team that belongs with capacity 1
- from team to table here I find trouble
- from table to sink with capacity 6
I don't know how to connect teams with tables without spliting the team into multiple tables