How to solve this variation of kirkkmans schoolgirls

Question

I am trying to implement an app which assigns s students to l labs in g lab groups. The constraints are:

1:students shall work with new students for every lab. 2:all

Answer 1

Constraint #1 alone is usually referred to as the social golfer problem. (Let parameters g be the number of groups and s be the size of each group and w be the number of weeks. A grouping is a partition of g * s golfers into g groups of size s. Determine whether w groupings can be found such that each pair of golfers are grouped together at most once.) The social golfer problem has been studied in the combinatorial optimization literature, and the approaches are of three types (you can use your favorite search engine to find the research articles):

1. Local search. This is effective when w is well below its maximum feasible value. Dotú and Van Hentenryck have a paper applying tabu search to the social golfer problem.

2. Complete search. This is necessary when w is above or just below its maximum feasible value but it does not scale very well.

3. Algebraic constructions. This is how the notorious g=8 s=4 w=10 instance was solved. Unfortunately, for many parameter sets there is no construction known.

To assign lab leaders, compute a maximum matching between students and lab groups, where there is an edge between a student and a lab group if that student belongs to that lab group.