CONSTELLATION
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Literature on Sports Scheduling
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CONSTELLATION GRAPH
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Glossario  
slot-number
CONSTELLATION - GLOSSARY, TERMINOLOGY and NAMING CONVENTIONS


slot-number
Glossary
CONSTELLATION - GLOSSARY, TERMINOLOGY and NAMING CONVENTIONS
by John Jan Popovic

For the teams enrolled in some Competition category will be created a fixture calendar.
A competition category can have one or more divisions/groups - A, B, C, D...
Each team must have assigned:
- Unique competition category name
- SchemeCode of Fixture Calendar
- division/group - A, B, C, D...
- a slot-number: 1, 2, 3.., 20

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The team's slot-number in division
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For example, if the number of teams in a division of a particular league is 16, (code-pattern F0 or F6) the competition takes place in 15 match-days.

Each of the 16 club-teams assigned to that division must have assigned a unique slot-number in division from 1 to 16. The assignment of the team's slot-number determines a unique fixture scheduler.

Fixture Calendar defines which team is playing with which team at which venue and when.

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Arbitrary and XY constrained slot-number
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For the teams of some clubs, the assigned slot-number of the team in the division grid can not always be arbitrary. For a team is said to be the BINDING team to one or more corresponding bound teams, (X or Y constrained).

If the grid - the number of the team's position in the group - is bound (or arbitrary), can be seen in CONSTELLATION GRAPH and can be calculated correctly only if the team master has already been assigned, or if there are all the data to make the algorithm Codegoni.


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calculating the BEST SLOT POSITION of Constrained team
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Algorithm for calculating the BEST SLOT POSITION of Constrained team - Codegoni method
- method to define the slot number/position for the constrained team

This calculator is used to determine the best team SLOT POSITION inside division grid for the constrained team, i.e. its SLOT POSITION Number depends on the following six parameters

CONSTRAINING Scheme code:
CONSTRAINING slot number:
constrained Scheme code:
pairing between the teams:
Week shift:
Matches season:


Team BINDING/PAIRING CONSTRAINTS concept is strictly related to the calculus of the optimal SLOT POSITION number sequence in the division roster for a constrained team.
One can say that a team has constrained slot position, when this team has pairing-binding constraints with some other team.
The SLOT POSITION in the division roster for teams of some clubs can not always be arbitrary.
Constellation scheduling considers team-binding, i.e. pairing constraints, are defined by the user in Constellation Graph.
X = SIMULTANEITY BINDING/PAIRING CONSTRAINTS
One can say that team1 and team2 have X-Binding:
- when t1 plays at home, then t2 plays at home
- when t1 plays away, then t2 plays away
One can also say that the team t1 is a travel partner of the team t2

Y = COMPLEMENTARITY BINDING/PAIRING CONSTRAINTS
We can say that t1 and t2 have Y-Binding:
- when t1 plays at home, then t2 plays away
- when t1 plays away, then t2 plays at home
When t1 plays home t2 plays away, and vice versa, we can also say that the team t1 is a complementary-travel partner of the team t2

The SLOT POSITION number in the division roster for a team, is either constrained or it is arbitrary/free.
It is defined in Constellation Graph where all desired fixture constraints for all teams are specified, and can be determined only if the constraining-team (master) was previously assigned in the division roster, i.e.
The constraining-team must have defined the SLOT POSITION number and the SchemeCode.
Or one can say that a team has constrained slot position, when this team has pairing-binding, with one other team of a higher category (master).

The SLOT POSITION number in the division roster for a constrained team depends on the following six parameters:
- CONSTRAINING Slot number, of the CONSTRAINING team
- CONSTRAINING SchemeCode, of the division where is situated the CONSTRAINING team
- Constrained SchemeCode, of the division in current grouping-assignment
- Binding/Pairing (x=concomitanza, y=alternanaza) between CONSTRAINING and constrained team
- Week-shift, weeks between CONSTRAINING and constrained competition season start (numero tra -8 e +8)
- Season

SchemeCode is a scheduler convention that allows precise definition of the home/away sequence of encounters/games among teams in the league for every single round. The unique slotNumber is associated to each team in the league/division.
SchemeCode is a two characters scheduler convention composed of: LETTER (Scheme) + NUMBER (Code)
The LETTER in the SchemeCode is exclusively determined by the number of teams in the league.
LETTER: X (2 teams), Q (3/4 teams), L (5/6 teams), I (7/8 teams), A (9/10 teams), C (11/12 teams), E (13/14 teams), F (15/16 teams), G (17/18 teams), H (19/20 teams)
NUMBER: Code6 or Code0 determine two complementary home/away series of encounters/games.
The 0-series and the 6-series of scheduler slots are differed from each other for a different but mutually complementary cadence of the pair of Home/Away encounters of all matches in the season.
For all constrained teams, the constrained SLOT POSITION number in the division roster, can be automatically calculated from the data defined in Constellation Graph.