MATCHINGS

1
MATCHINGS
A college dramatic society has six
helpers Andrew, Donna, Henry, Karl, Nicola and
Yana. They are to be matched to six tasks Props,
Lighting, Make-up, Sound, Tickets and Wardrobe.
The table indicates which tasks each person is
able to do.
2
As N is unmatched, we use N as the starting point
of an alternating path.
As Y is unmatched, we use Y as the starting point
of an alternating path
This is represented by the following Bipartite
Graph
Initially, Andrew, Donna, Henry Karl are
matched to the first task in their list.
N ? S K ? L H ? M
Y L K W A P
BREAKTHROUGH
Change status
N S K L H M
Change status
Y L K W A P
N can do S
We apply the algorithm once more to improve the
matching
S is being done by K
Add NS, KL, HM
Add YL, KW, AP
K can do L
Remove SK, LH
Remove LK, WA
L is being done by H
H can do M
BREAKTHROUGH
This is a maximal matching
All 6 people are now matched to 6 different jobs
We now have 5 people matched
3
Remember to state the final matching when you
have finished
Andrew Props Donna Tickets Henry
Make-up Karl Wardrobe Nicola Sound Yana -
Lighting