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CONSTELLATION GRAPH  
Glossary > CONSTELLATION GRAPH
by John Jan Popovic


Glossary > CONSTELLATION GRAPH
by John Jan Popovic

The experience with the definition and programming of sport schedules provided the insight that one should avoid complexities of control and concentrate on organizing the data to reflect the real requirements of the schedule constraints.

To solve problems of ambiguity and incompleteness of the manual constraints definition and programming of sport scheduler fixtures, I have invented a data structure denominated CONSTELLATION GRAPH. It contains the all information in a clear and non ambiguous fashion about the club's teams constraints. In the CONSTELLATION GRAPH many data are already pre-inserted automatically as default values which are stored in competition card records. CONSTELLATION GRAPH contains the all information of all team's competitions, allowing easy handling and manipulation of sports-field-venues timetable constraints and team's mutual complementarity dependences, even among the teams of different clubs.


No ambiguity can arise, because CONSTELLATION GRAPH provides a means of expression for exploring scheduling requirements, that would otherwise be too complex to deal precisely.


The Constellation Graph is a dynamic form with with a lot of default data. It has an intuitive interface. It is an ordered list of the teams represented in a table, where you can easily manipulate the preferential week days and times on the venue fields of teams' matches.
Also it has an interface for a formal syntax notation that allows a precise definition of the desires of matches between the complementary teams that play on the same day, even between the teams of different clubs.

CONSTELLATION GRAPH is also a framework for thinking and exploring of the constraints of the match fixtures.

CONSTELLATION GRAPH creates recommendations for the compilation of data, not requiring an experienced user to define and/or modify these arrangements. Fixtures of the teams on the fields are intuitively defined through the CONSTELLATION GRAPH and via CONSTELLATION STADIA/VENUE TIMETABLE.

CONSTELLATION GRAPH features:
* Selection of stadia venues
* Intuitive editing of time and week days for the matches
* Easy to set and explore Complementary Bindings constraints
* Efficient fixture definition
* Non ambiguous - consistent data structure
* Complete and non redundant fixtures

Compilation of CONSTELLATION GRAPH is an easy and intuitive activity.
The teams which have complementarity binding constraints, usually belong to the same CLUB (but it is not always the case). In rare cases, there may be present external binding constraints between the teams of different clubs. The binding constraints between teams from different clubs are defined with particular formal syntax rules (Multigraph Link Syntax / MGL).

The BINDING constraints
Complementarity(Y), simultaneity(X) and non-simultaneity(Y) team-bindings

For the teams it is said to have simultaneity-binding constraints (X), only if they play TOGETHER in the same day, all AWAY or all at HOME.

For the two teams it is said to have complementary-binding constraints (Y), if one team has match at home, while the other plays away. Teams t1 (X) and t2 (Y) must have complementary schedules, i.e. when t1 plays home t2 plays away, and vice versa.

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The BINDING (MASTER) and bounded/constrained (SLAVE) teams
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Sometimes the team slot positions in a league/division can not always be arbitrary. For a team is said that is the BINDING team corresponding to one or more constrained teams, which are bonded whether in simultaneity (X) or complementarity (Y) with it.

If a team's slot positions number in a league/division grid - is X or Y constrained (or arbitrary), we can see it easy in the CONSTELLATION GRAPH.
Its correct slot number sequence can be consequently correctly calculated, only if to its BINDING MASTER team are already assigned the slotNumber and schemeCode values, i.e. there should be present all input data for the Codegoni algorithm.

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The input parameters for the calculation of the Codegoni algorithm
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Codegoni algorithm calculates the best slot position of the constrained team which has simultaneity (X) or complementarity (Y) binding constraints.

That is to say that the slot position of a team is constrained (slave), when it is bonded whether in simultaneity (X) or complementarity (Y) with one constraining BINDING team (master). At this point the slot position in a league/division grid (and the alternative sequence of slot positions secondary choices) of the bonded team of a less important competition depends on six parameters.

First three parameters are the parameters of the master team, and they should have been previously manually defined, or in some cases automatically assigned.
It can be proceeded with the composition of the division/leagues, only if each of these three parameters has been previously automatically assigned, or manually defined.

1) Scheme Code of the superior team
2) Slot Number of the superior team
3) Binding (x, y) between the teams

The following three parameters are established automatically during the splitting process of of the competition into divisions/leagues.

4) Constrained Scheme Code
5) Week shifts between superior and constrained team(number between -8 and +8 weeks)
6) Master team matches season (outward or return, but usually it is outward)

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

CONSTELLATION MULTIGRAPH

The Constellation Graph of a club can be easily linked to the other club's graphs teams. The external multigraph links are automatically re-embedded in the constellation graphs of all other externally coupled teams.


External Binding/ Multigraph Link

To solve the problems of complementarity binding constraints between teams of different clubs, I have introduced a formal notation called Multigraph links. Multigraph is a link notation with a formal syntax, which describes couplings between the teams of different clubs.

There are two types of external constraints - Multigraph link, and both are stored in external_constraints field of the team nodes in Constellation Graph: (MGL_SLAVE POINTER MULTI) and [MGL_MASTER POINTER].

(MULTI MGL_SLAVE POINTER) is described in parentheses () and must be entered manually by the user, while the [MGL_MASTER POINTER] is described in the angular brackets [], and is automatically added.

# Multigraph MASTER SYNTAX -- external master team
it must be entered manually by the user
(matricola_slave:abbinamento:elenco_squadre)

# Multigraph SLAVE SYNTAX -- externally bonded slave team
it is automatically added by the system
[675630:y:3:6:E0:24.1]
[matricola_master:abbinamento:nodo_master:griglia_master: schema_master: gerarchia_master]


The FORMAL REGISTRATION OF EXTERNAL COUPLINGS
(matricola: abbinamento: lista_nodi_vincolati)


In the vast majority of the clubs is sufficient to define the bindings between teams from the same club; and this is quite simple and intuitive: by specifying the nodes X and Y of a graph.

When user wants to describe a couplings (x, y) between teams of different clubs he must use the formal notation called Multigraph Link. MGL must be entered in the field external_notes of the binding (master) team. And it affects all externally bonded slave teams of an another club.
The (slave) teams are located in another Constellation Graph, and field notes - couplings external, this graph can be seen [data binding team-master] in the brackets. These external couplings are placed to the teams entered in the Constellation Graphs automatically, without user intervention.