ROUND ROBIN SCHEDULING

BYNAGA SAI HANUMAN.POTTI

OUTLINE

• What is Round Robin.

• Complete graph.

• Real time Example.

• Relation to graph problem.

• Depicting graph solution.

• Graph colouring.

WHAT IS ROUND ROBIN?

A round-robin story is one that is started by one person and then continued successively by others .It is an arrangement of choosing all elements in a group equally in some rational order in turn.

A round robin format is problematic when the number of entries is high. For example, a tournament with 32 entries would take 496 games to complete using a round robin.

ROUND ROBIN

SINGLE DOUBLE

A round-robin tournament is one in which every player plays against everyone else once. For

example, with 3 players, we will have 3 matches: A-B, B-C, C-A. How many matches are needed for

4 players?  5 players? N players? 

If we can schedule two matches in the same time slot (round), how many rounds will it take for a 3-

player round-robin tournament? 4-player tournament? 5-player tournament? 

Complete graph: complete graph is a graph in which every pair of distinct vertices

connected by an edge.

K7::COMPLETE GRAPH WITH 7 VERTICES1

2

3

45

6

7

Real time example:

Lets take an indian premier league(IPL)- cricket tournament and let it consists of 4 teams .

Team 0-----Deccan chargers.

Team 1-----chennai super kings.

Team 2-----kolkata knight riders.

Team 3-----Mumbai indians.

Problem relating to graph: let us take a tournament with 4 teams (0,1,2,3).By using round robin we will depict the number of

matches ,number of rounds and the teams involved in each round.

1

2

3

0

0,1 0,2

2,3

1,3 1,2

0,3

Round Robin Graph Matches between teams

NUMBER OF ROUNDS

We have n teams, and all teams play

all others m times in m(n – 1) rounds.For single round robin: m=1 if n=4,i.e. 4 teams 3 rounds.

For double round robin: m=2 if n=4,i.e. 4 teams 6 rounds.

0,1 0,2

2,3

1,3 1,2

0,3

Matches between teamsCalculate number of matches

Case 1:Single Round RobinFor n teams =n(n-1)/2

Case 2:Double Round Robin For n teams=2*(n(n-1)/2)=n(n-1)

• graph colouring problem or vertex colouring problem involves assigning colours to each vertex v Ɛ V such that no pair of adjacent vertices is assigned the same colour and the number of colours used is minimal .

• The minimum number of colours required to colour a particular graph is called the chromatic number".

Graph colouring:

0,1 0,2

2,3

1,3 1,2

0,3

Assigning matches in each round :

0,1 0,2

2,3

1,3 1,2

0,3

ROUND 1st match 2nd match

1 (0,1) (2,3)

0,1 0,2

2,3

1,3 1,2

0,3

ROUND 1st match 2nd match

2 (0,2) (1,3)

ROUND 1st match 2nd match

3 (0,3) (1,2)

ROUND 1st match 2nd match

1 (0,1) (2,3)

2 (0,2) (1,3)

3 (0,3) (1,2)

Round robin schedule:

For 10 teams:

References

http://en.wikipedia.org/wiki/Round-robin_tournament.

www.rhydlewis.eu/talks/sportsRRTalk.pdf. www.splendidcity.net www.tutorialspoint.com/...system/os_process

_scheduling_algorithms.htm.