I have a problem which is a variation of the Sports League Scheduling Problem. This problem pertains specifically to a tennis league at my own sports club. Each winter, the pro puts out a blank sheet of paper for people to sign up for tennis leagues. From year to year, the number of people who sign up fluctuates; however, the number of tennis courts available stays the same at 4 courts. For my particular problem, lets say that 12 people sign up for the league (this is a singles league) so each week, 4 people will have byes and 8 will play. Can anyone come up with an algorithm which allows each player to play each other player 1 time only and also deals out a fair number of bye weeks to each player? Assume the league runs until every player has played every other player once. If anybody can come up with such an algorithm, would it scale well to years when a different number of players signed up?
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