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


CONSTELLATION GRAPH
The Constellation Graph is constraint visualisation and modification tool.

CONSTELLATION GRAPH is a framework for thinking and visualisation of constraints and match preferences of the teams of a club. CONSTELLATION GRAPH provides a means of expression for precise description and visualisation of preferences and commitments (i.e. preferential times and days of matches) of the teams on the venues/fields.

In order to solve the ambiguity, vagueness and incompleteness of various paper forms where informally are defined team's home/away requirements and other preferences of the teams of a club, I have invented a formal data structure denominated CONSTELLATION GRAPH.

It contains all clear and unambiguous information about the teams of the club. In CONSTELLATION GRAPH many data are already automatically pre-inserted, allowing easy handling of the constraints relating to commitments on sports and unambiguous definition and unambiguous pairing/binding between the teams with home/away requirements.

The Constellation Graph is an interactive form, an ordered table of teams, where one can easily select and manipulate the match-days of and preferential play-time as well as the choice of the field and venue.

Also it has a formal syntax interface that allows a precise definition of pairing/binding constraints between the teams playing in the same match-day. Binding constraints between the teams of different clubs can also be specified with formal syntax that allows a precise definition of pairing/binding constraints for home/away requirements.


In order to solve the challenges of ambiguity and incompleteness that arose in compiling obsolete paper forms where preferences of the teams are compiled by clubs during the enrolment of the teams to championships, I have invented CONSTELLATION GRAPH.
It is an intelligent interactive form with intellisense features.

CONSTELLATION GRAPH creates interactive "intellisense" suggestions for the compilation of data. It does not require a skilled operator to describe and edit these arrangements, preferences and commitments of the teams on the fields/venues.
For sport league organisers and operators, it is a powerful intuitive instrument which can express, explore and manipulate match preferences and constraints of the teams.

CONSTELLATION GRAPH is:
* Easy to consult
* Easy to check
* Easy to edit
* Efficient
* Intuitive
* Non ambiguous - coherent
* Compiling the CONSTELLATION GRAPH is effortless and intuitive

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A reservation request
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Constellation Graph fully replaces, outdated, ambiguous, incomplete and confusing obsolete paper form for specifying XY pairings/bindings and time-table preferences of teams. It also displays many other data and has many other useful interactive features: enabling user-friendly, intelligent data entry manipulation and XY binding-constraints between the teams.

During the enrolment-subscription of of teams to competitions for the season, a Club should specify times, days and preferential fields/playgrounds, as well as the preferences of X simultaneous / Y alternative pairing between the teams of the club.

It is a reservation request of the team on the field, where the club usually specifies:
* The preferential match-times of the teams on the venues/fields
* the constrained XY pairing-binding between the teams

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Internal and external bindings
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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 - i.e. external constraints.
Most of times binding-constraints are internal, i.e. between teams of the same club.

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

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External bindings
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To solve the problems of XY binding constraints between teams of different clubs, I have invented a formal notation called Multigraph binding. Multigraph binding is a formal syntax notation, which describes the XY binding constraints between the teams of the different companies.

There are two types of Multigraph binding constraints:
- (SLAVE MULTI POINTER) -
- [MASTER POINTER] -

(external SLAVE MULTI POINTER) is defined between parentheses () and must be entered manually by the operator in the Constellation graph.
# Multigraph MASTER SYNTAX -- constrained teams are external
(slave_club_number: binding: constrained_teams_list)

While [External MASTER POINTER] is described in the [] brackets, and is inserted automatically.

# Multigraph SLAVE SYNTAX -- CONSTRAINING team is external
[675630:y:3:6:E0:24.1]
[master_club_number: binding: master_node: master_slot_number : master_scheme_code: master_team_hyerarchy]

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X-constraints
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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 at together at HOME venues.

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

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BINDING and bounded teams, i.e. MASTER and slave teams
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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) CONSTRAINING SchemeCode
2) CONSTRAINING slot-number
3) Binding (x,y) between the constraining (master) team and the constrained (slave) team
Second three parameters are the parameters that are established automatically during the process of subdivision of the teams of the competition into the divisions/groups.
4) SchemeCode of the constrained (slave) team
5) Week shift (between -8 and +8 weeks)
6) Matches season (outgoing or return matches)


A constrained (bonded, slave) team can have one and only one corresponding BINDING (constraining, master) team. While a BINDING (master) team can have many bounded teams (slaves), of the same or lower hierarchical level, both of the same or different club.


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CONSTELLATION MULTI-GRAPH for external bindings
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The Constellation Graph of a club can be easily connected/ bonded to the other Constellation graphs of other clubs. The Multigraph-links represent external binding constraints -- between the teams of different clubs.

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External Binding/ Multigraph binding
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To solve the problems of XY binding constraints between teams of different clubs, I invented a formal notation called Multigraph binding. Multigraph binding is a formal syntax notation, which describes the XY binding constraints between the teams of the different clubs.

There are two types of Multigraph binding constraints:
- (SLAVE MULTI POINTER) -
- [MASTER POINTER] -

(External SLAVE MULTI POINTER) is defined between parentheses () and must be entered manually by the operator in the Constellation graph in the "External Constraints"



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FORMAL NOTATION FOR EXTERNAL BINDINGS
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(slave_club_number: binding: constrained_teams_list)

For the vast majority of clubs it is sufficient to describe the Home/Away xy binding of teams for the sameclub in the Constellation Graph. This is quite simple and intuitive: specifying the nodes X and Y of a graph.


# Multigraph MASTER SYNTAX -- constrained teams are external
(slave_club_number: binding: constrained_teams_list)

While [External MASTER POINTER] is described in the [] brackets, and is inserted automatically.

# Multigraph SLAVE SYNTAX -- CONSTRAINING team is external
[675630:y:3:6:E0:24.1]
[master_club_number: binding: master_node: master_slot_number : master_scheme_code: master_team_hyerarchy]

Instead, when the operator wants to describe a (x, y) binding between teams of different clubs, he must use the formal notation called Multigraph Binding.



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CONSTELLATION GRAPH columns
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The first column / node number indicates the consecutive number of teams in the graph (serves for consultation only)
The column 2 indicates the registration number of the club (serves for consultation only)
The column 3 shows the category and competition name (serves for consultation only)
The column 4 shows the field (drop-down menu, there are only the fields surveyed by the club in question)
The column 5 indicates the start-constraint, i.e. the team start season playing home or away (not used in this release)
The column 6 indicates the start date of the competition (this information is automatically detected by the card on competition, so it should be written only once, if you want)
The column 7 indicates the week-day of the game (Saturday, Sunday)
The column 8 indicates the time of the meeting (this information is automatically detected by the card on competition, so it should be written only once, if you want)
The column 9 is for consultation-only, it depends on columns 11 and 12 (Combined and Splitting)
The column 10 is for consultation-only, it depends on the columns 11 and 12 (Combined and Splitting)
The column 11 indicates the node-numbers of teams playing in X binding
The column 12 indicates the node-numbers of teams playing in Alternating Y binding
The column 13 indicates External Constraints notes
The column 14 indicates the number or letter of the division/group
The column 15 indicates the slot-number of the team
The column 16 indicates the SchemeCode adopted for the competition of the team
The column 17 indicates the competition hierarchy is for consultation-only, (serves us to complete the algorithm processing module Calendars).
The column 18 indicates the number of islet-number of the Constellation graph (also serves for consultation only)


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Constraints: collection of conditions that must be fulfilled by scheduling solutions to be found. Constraints are rules user creates at design-time. Constellation Constraints are nothing but the rules on the scheduling data.
Special constellation software mechanism gets set of constraints and returns solutions. What data is valid and what is invalid can be defined using constraints graph. The Constellation Graph is the computerized logical representation of a conceptual (desired scheduling) model, consisting of a set of formal scheduling rules.