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Glossary > Schedule SchemeCode
CONSTELLATION - GLOSSARY and NAMING CONVENTIONS


Glossary > Schedule SchemeCode

by John Jan Popovic

We address the problem of scheduling the matches of a balanced round robin tournament for a sport league.
Practical results show that the optimal solution of the assignment problem can be found in reasonable time, despite the fact that the problem is NP-complete.



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.

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An example -- SchemeCode I6
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For example, if the number of teams in a division of a particular league is 8 (n), there are 4 (n / 2) host teams and 4 (n / 2) hosted in any match day.
The host teams play at HOME, while those hosted out, ie in AWAY.

For example, the slot number arrangement for SchemeCode I6 of the FIRST Match Day looks like this:

Home: Away
01: 07
02: 06
03: 05
04: 08

In the first Match day, the teams in the left column: 01,02,03 and 04 play at HOME, against teams in the right column: 05, 06, 7:08, playing away (OFF-house).

For CODE 6 The host teams which play at HOME venues have LOW SLOT NUMBERS (applies only for the first day of the championship)
For CODE 6, the hosted teams are playing AWAY have HIGH SLOT NUMBERS (applies only for the first day of the championship)

For any match-day, if you know the team's SLOT NUMBER in the GRID and SCHEME CODE, you can uniquely determine the HOME/AWAY sequence.

It can be said also, that START-VENUE (HOME/AWAY) is a function of two variables: SLOT NUMBER and SCHEME CODE.
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Team Slot Number /Team Roster Position
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Se ad esempio il numero di squadre in un girone di un particolare campionato è 16, (schema-codice F0 oppure F6) il campionato si svolge in 15 giornate. Ad ognuna delle 16 squadre-società deve essere associato un univoco Numero di GRIGLIA nel girone da 1 a 16.

Balanced ROUND ROBIN
L'assegnazione del Numero di GRIGLIA determina un univoco Calendario di Competizioni, ovvero quale squadra gioca contro quale ed in quale giornata – la cadenza dei incontri.
Nota bene:
Il numero totale delle possibili PERMUTAZIONI in questo esempio è 16!. (sedici fattoriale) 16 ! = 2.09227899 × 1013, oltre 20 trilioni di possibili PERMUTAZIONI.

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SchemeCode scheduler convention
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SchemeCode is a scheduler convention that allows precise definition 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 formed by: LETTER + NUMBER
The LETTER in the Scheme code 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 series of encounters/games. The 0-series and the 6-series of scheduler slots are differed from each other for a different and mutually complementary cadence of the pair of encounters Home/Away.



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ASSEGNAZIONE - COMPOSIZIONE GIRONI
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Il programma Constellation premete di assegnare alle squadre di una particolare competizione un univoco Numero di GRIGLIA nel girone, lo Schema Codice del girone e la Lettera di Girone in una maniera intuitiva ed inequivocabile.
L’operatore può manipolare il numero delle griglie delle squadre, mentre il calendario del campionato la Constellation compone automaticamente, usando l'algoritmo Balanced Round Robin.
Lo Schema Codice Griglie serve per stabilire precisamente i parametri del algoritmo Balanced Round Robin per la redazione automatica del calendario-partite. La definizione della cadenza Casa/Fuori del svolgimento di incontri dipendono dal numero di GRIGLIA associato in una maniera univoca ad ogni squadra nel girone e dallo stesso Schema Codice del girone.
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Calendario incontri di una particolare Competizione
Il calendario incontri è un elenco di tutte le partite del campionato di una competizione.
I Calendari descrivono tutte le partite del campionato: (Chi gioca, Dove si gioca, Quando si gioca)
a) Elenco squadre che competono tra loro (la Società ospitante e la Società ospitata),
b) Elenco Campi Sportivi dove si gioca,
c) Giornata quando si gioca (Giorno, data e orario di gara)

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Ovviamente, l'operatore deve stabilire previamente quale è la DATA della prima GIORNATA DI GARA del girone d’andata, per la COMPETIZIONE in formazione.
Una volta decisa la DATA D'INIZIO della prima GIORNATA DI GARA per la COMPETIZIONE in assegnazione, CONSTELLATION determinerà automaticamente quale sarebbe il CODICE OTTIMALE da applicare durante l'assegnazione delle squadre di questa competizione.


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Constellation includes all instruments for creation of high quality sport-event schedulers. Constellation is supporting a diversity of arrangement algorithms (Balanced ROUND ROBIN scheduling) and analysis built-in instruments to enable creating sport schedules easier than ever.
Constellation Scheduling Algorithms & Reports
Constellation scheduling considers user predefined playground, time and team-binding constraints, which are user predefined in Constellation Graph in Constellation Census module
Constellation Graph enables quick and simple management of team-binding, time and stadium-location constraints settings
Constellation schedules tend to obey particular constraint logic definitions (defined via Constellation Graphs )
Constellation advanced scheduling algorithm will automatically generate competition schedules with a more efficient and compact match calendars
All matches for each week are automatically generated, and constraints are conformed to each schedule week, in order to provide a harmonious distribution of teams and playground locations during the sport season
Inter-divisional conflict resolution: conflicts are automatically resolved across all divisions/groupings during the interactive schedule creation.
Constellation has incorporated support for balanced round robin schedules, Swiss round, single and double elimination tournaments, mixed (inter) divisional schedules.
Scheduler match days in successive rounds do not necessary have to be in a fixed week day; i.e. matches in different rounds can take place in a user modifiable week day.
Constellation has support for groupings of multiple competition schedules in order to follow conflicts and manage inter-divisional play
Competition schedule calendar in an HTML file.
Report includes list of games per team in each round, list of home and away games, home/away sequence for each team, a confrontation diagram describing the game list each team plays versus it's rivals.
Schedule reports allows filtered viewing of games for defined competition, team or date, with information sorted in the proper chronological order.

Abstract:
Introduction Sports scheduling is an area of increasing interest in constraint programming. As amateur and professional sports leagues proliferate and grow in size and complexity, organizers are increasingly turning to computer assisted scheduling [Nemhauser and Trick]. The scientific literature in this area is also growing and one can begin to get a sense of the range and mathematical difficulty of the problems encountered. These can include classical challenges such as set covering problems and quadratic assignment problems. In this note we concentrate on a version of a core problem that invariably comes up: determining whether a set of constraints on the schedule is feasible. This is often called the "timetabling" problem of the scheduling process. Here we consider the timetabling problem for a "round robin" schedule: the case in which every team must play every other team exactly once. (Later we will discuss related problems that come up in other sports situations such as
Generating a schedule for a professional sports league is an extremely demanding task. Good schedules have many benefits for the league, such as higher incomes, lower costs and more interesting and fairer seasons. Many solution approaches for sports scheduling problems have been introduced in recent years. Even if quite efficient algorithms have been designed, there exist not many cases where academic researchers have been able to close a contract with a sports league owner.
This web site presents an overview of the sports scheduling problem, a set of standard benchmark instances and the best solutions obtained for these instances. The instances are divided into two categories: artificial test instances and real-world instances. We hope that these instances will help researchers to test the value of their solution methods.

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2. Tournament Scheduling
A league comprises 2n teams, and in 2n ?? 1 consecutive rounds each team must play with each other. Matches take place at the home stadium of one of the two teams, and home and away games should be alternated as much as possible. We call break, after de Werra (1980), the fact that a team plays two consecutive rounds in the same location, where the term location denotes either home or away. The problem is to nd a schedule scheme that minimizes the number of breaks and satisfies a number of other side constraints.

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CONSTELLATION SCHEDULER FEATURES
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Flexible Scheduling
Constellation Scheduler takes care of balancing game times and locations across the teams. And gives you the flexibility to enter max games per day and per week, min days off between games, and number of times each teams plays each other. Our software handles multiple venues, division play, and game and team constraints and exception processing.
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