We have n people and split them up in groups of size x. Each group of x people goes to lunch together. Next time around when the groups are set up people who were in a group last time should not end up in a group together if avoidable. Ideally they also should go out with as few people from the time before that.I thought about modelling this as a graph problem:People are vertices $v \in V$ and going to lunch together creates a edge between those vertices. The edge has a weight on it that's higher the more recent the lunch happened. Now we want to create $\frac{|V|}{x}$ subgraphs with x vertices each and minimize the sum of the edges connecting the vertices in each subgraph.Is there a name (lunching programmers ? ;-) ) and associated research for this problem? Or is there a way to map this to another known problem?
Sending people to lunch together with minimal repetition
graph theory;co.combinatorics;optimization