The coordinator of a local golf club has come to you with the following problem. In her club, there are 32 social golfers, each of whom play golf once a week, and always in groups of 4. She would like you to come up with a schedule of play for these golfers, to last as many weeks as possible, such that no golfer plays in the same group as any other golfer on more than one occasion.
Possible variants of the above problem include: finding a 10-week schedule with 'maximum socialisation'; that is, as few repeated pairs as possible (this has the same solutions as the original problem if it is possible to have no repeated pairs), and finding a schedule of minimum length such that each golfer plays with every other golfer at least once ('full socialisation').
The problem can easily be generalized to that of scheduling m groups of n golfers over p weeks, such that no golfer plays in the same group as any other golfer twice (i.e. maximum socialisation is achieved).
We consider the generalization to m groups of n golfers over p weeks.
DATA (on file dat):
- groupSize, nbGroups, nbWeeks are the problem input;
- nbGolfers=groupSize*nbGroups is derived by the input with obvious semantics.
- Search space is modeled by predicate plays(W, G, P) which means that P plays in group G at week W
c1 - Each golfer is part of exactly one group in each week;
c2 - Each group has exactly groupSize golfers;
c3 - Each pair of golfers only meets once.
Marco Cadoli, Toni Mancini, Davide Micaletto and Fabio Patrizi
Dipartimento di Informatica e Sistemistica, UniversitÓ di Roma "La Sapienza"
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