Round Robin Scheduling Algorithm

Report
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.
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 3player round-robin tournament? 4player 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.
Round Robin Graph
Matches between teams
1
0,1
0
2
0,3
2,3
1,3
3
0,2
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
Matches between teams
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)
0,1
0,2
0,3
2,3
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".
Assigning matches in each round :
0,1
0,1
0,2
0,3
2,3
1,3
1,2
0,2
0,3
2,3
1,3
1,2
0,1
0,2
0,3
2,3
1,3
1,2
ROUND
1st match
2nd match
1
(0,1)
(2,3)
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/Roundrobin_tournament.
 www.rhydlewis.eu/talks/sportsRRTalk.pdf.
 www.splendidcity.net
 www.tutorialspoint.com/...system/os_process
_scheduling_algorithms.htm.

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