Related Topics
Glossary
Naming conventionts
CONSTELLATION GRAPH
Slot number
XY binding-constraints
Types of constrained teams in Constellation Graph
Constellation Census
CONSTELLATION  
XY binding-constraints
scheduling the teams with home/away requirements


XY binding-constraints
by John Jan Popovic


XY binding-constraints are related to scheduling the teams with home/away requirements. The binding constrained teams usually belong (but not always) to the same club.
In the rare cases, there may be present also external binding-constraints between teams of different clubs.
Most of times binding-constraints are internal, i.e. between teams the same club, which has completed enrolment


XY binding-constraints between the teams
X-Conjunction and Y-Complementary binding-constraints

X-constraints
For teams is said to have X-CONJUNCTION binding-constraint (annotation X), only if master team plays in X-CONJUNCTION on the same day, or all together AWAY, or all together at HOME venues. BINDING and bound teams play all together AWAY.
Or BINDING and bound teams play all together at HOME venues.

Y-constraints
For teams is said to have Y-ALTERNATE (annotation Y), if on the same match-day, a master BINDING team plays at home, while the Y-constrained bound teams are playing away -- and vice versa.


BINDING and bounded teams, i.e. MASTER and slave teams
----------------------------------------------------------------------------
For the teams of some clubs, the slot-position of the team in the division can not be arbitrary. For a team is said to be the BINDING team for one or more corresponding bounded teams, whether it has X or Y constraints.


That is to say that the slot-position of a team is bounded (constrained), when it has X or Y constraints. At this point the slot-position of a team in a group-division depends on six parameters:
1) SchemeCode of the master team
2) slot-number of the master team
3) Binding (x,y) between the constraining (master) team and the constrained (slave) team
Secondi tre parametri sono i parametri che si stabiliscono in automatico durante il processo di SUDDIVISIONE della competizione nei gironi.
4) SchemeCode of the constrained (slave) team
5) Week shift (between -8 and +8 weeks)
6) Games (outgoing or return matches)

------------------------------------------------------
Constellation Constraint Definition Language
-------------------------------------------------------
a) Complementarity, Y-binding: Teams t1 and t2 must have complementary schedules (i.e. 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).
..........................................................................................................
b) CDL:O, Non simultaneity among the teams of the same Insulae
..........................................................................................................
Non simultaneity & O-binding: Three or more teams t1, t2, and t3,... cannot be simultaneously in the same location, only one of teams X (home), while all others are Y (away)
* O - non simultaneity among the teams of the Insulae


Constraints a) and b) are always easily defined in Constellation Graph and often I.e, while the constraints c), d) and e) must be defined externally via CCDL (Constellation Constraint Definition Language)
.........................................................
APRIORI FIXED SLOT NUMBERS
.........................................................
c) CDL:H@7R
Availability: Team t must play home (or away) at round n.
* H@7R - team must play home at round 7

d)
Non Availability: Team t cannot play at round n (day, time). Riposo (Bye) at round n.
*B@5R - Bye game at round 5

e) Mating exclusion: Team t1 cannot play home (or away, or both) with team t2 at round n.
*XH@3R, t1 - Team cannot play home with team t1{club_number:node_number} at round 3.

f) Compulsory Mating: this team must play home (or away, or both) with team t2 at round n.
*Ch@5R, t1 - Team must play home with team t2{club_number:node_number} at round 3.
----------------------------------------------------
Hard and soft complementarity constraints
----------------------------------------------------
Hard complementarity constraints are used if two teams share the same stadium
(e.g. the "San Siro" stadium in Milan is shared by Internazionale and A.C. Milan).
Soft complementarity instead is used if the stadia of two teams are located close to each other and the clubs want to optimize the use of railways and highways for their supporters (e.g. Feyenoord and Sparta have their stadia in Rotterdam).
The constraints I.c, I.d and I.e must be defined externally via CCDL (Constellation Constraint Definition Language) and are actually interpreted as constrained_slot_number(s) of the team.


================================================================
C6 Example
================================================================
Competition calendar for: Esordienti I Anno 2000 a 9 Milano
Division/League: [A]
SchemeCode cadence: C6
..............................................................................................................................
Slot Number --Team Outward matches Cadence -- Home[C]/Away[F]
............................................................................ 1 2 3 4 5 6 7 8 9 10 11
C6 [1] A.S. C.O.B. 91 (79921).............................. H A A H A H A H A H A [1]
C6 [2] U.S. ATLETIC TREZZANO (65243)............. H A H A A H A H A H A [2]
C6 [3] S.S.D. AUSONIA 1931 (57838).................. H A H A H A A H A H A [3]
C6 [4] POL. LOMBARDIA UNO (675071) [F]......... H A H A H A H A A H A [4]
C6 [5] A.S. CALVAIRATE (8780)........................... H A H A H A H A H H A [5]
C6 [6] A.S.D. ABBIATEGRASSO (62145)............. H A H A H A H A H A H [6]
C6 [7] F.C. ANDICE PIOLTELLESE (675763)........ A H H A H A H A H A H [7]
C6 [8] A.S. AICS OLMI (675113)........................... A H A H H A H A H A H [8]
C6 [9] POL. BUCCINASCO (676162)..................... A H A H A H H A H A H [9]
C6 [10] CALDERARA (203666) [A]........................ A H A H A H A H H A H [10]
C6 [11] A.C. BRUZZANO (8020)............................ A H A H A H A H A H A [11]
C6 [12] G.S. VILLA (33480) [B]............................. A H A H A H A H A A H [12]

http://www.constellationsystems.net/calendario2015_milano/EsordientiIAnno2000a9.html