ROUND ROBIN SCHEDULING

BY NAGA 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.

SINGLE

ROUND ROBIN

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.

1

K7::COMPLETE GRAPH WITH 7 VERTICES

7 2 6 3 5 4

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.

0 Round Robin Graph 1 2 3 2,3 Matches between teams 0,1 0,2 0,3 1,3 1,2

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.

Calculate number of matches

Case 1:Single Round Robin For n teams =n(n-1)/2 Case 2:Double Round Robin For n teams=2*(n(n-1)/2)=n(n-1) 2,3 Matches between teams 0,1 0,2 0,3 1,3 1,2

Graph colouring:

• •

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".

2,3 0,1 1,3

Assigning matches in each round :

0,2 0,1 0,3 2,3 1,2 1,3 0,2 1,2 0,3

2,3 0,1 1,3 0,2 0,3 1,2

ROUND

1

1 st match

(0,1)

2 nd match

(2,3)

ROUND

2

1 st match

(0,2)

2 nd match

(1,3)

ROUND

3

1 st match

(0,3)

2 nd match

(1,2)

ROUND

1 2 3

1 st match

(0,1) (0,2) (0,3)

2 nd match

(2,3) (1,3) (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

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www.tutorialspoint.com/...system/os_process _scheduling_algorithms.htm

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