The Sports League Scheduling Problem is a combinatorial search problem that involves scheduling unique pairs of one resource ("teams") within a certain number of rounds while uniquely using or visiting another resource ("fields" or time "periods"), usually according to one or more additional constraints. The Howell movement and Mitchell movement schedules of Duplicate Bridge tournaments are one example.
The Sports League Scheduling Problem is a function problem with complex and variable constraints usually addressed with combinatorial search algorithms.
A long-standing practical example of this is the constraints of developing schedules for Duplicate Bridge tournaments including the Howell and Mitchell scheduling movements of Duplicate Bridge tournaments which address different variants of this problem. It is in fact a type Combinatorial Search problem that has had some work on mathematics and computer science papers over the years(see: 1, 2, and 3)
Although there are many variants, the base problem is to arrange ("schedule") some group of things ("teams") in pairs (a "game", "match" or "event") within a rectangular array of a scheduling time (a "round") and a unique resource (a "period", "field", or in Bridge "boards"). This has to be done within the following common minimum constraints:
- Teams cannot play themselves.
- Teams cannot play more than once in the same round.
- Fields cannot be used/(played on) more than once in the same round.
Typically, the following two minimum constraints are also common (though some obscure variant problems may change these):
- Teams cannot play on the same field more than once.
- Teams cannot play the same team more than once.
After these almost universal rules, there are a multitude of additional possible constraints which produce all of the many variants of this problem. Typical additional constraints may include:
- Byes may be allowed, disallowed or every team may be required to have a specified number of byes.
- Every field may be required to be used every round, or required to be unused in a specified order.
- The number of teams, rounds and fields may each be specified and/or have a fixed relationship to each other such as the number of teams is twice the number of rounds, etc.
