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Matroids and Matchings
The structure that makes the greedy algorithm correct, and the matching theory of Hall and König that mirrors it.
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Run greedy on the triangle
K
3
K_3
K
3
with edge weights
w
(
a
b
)
=
3
w(ab)=3
w
(
ab
)
=
3
,
w
(
b
c
)
=
2
w(bc)=2
w
(
b
c
)
=
2
,
w
(
c
a
)
=
1
w(ca)=1
w
(
c
a
)
=
1
.
What is the weight of the maximum-weight spanning tree it returns?
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w
( )
x
n
√
⌫
AC
7
8
9
+
4
5
6
−
1
2
3
×
0
.
a
b
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